37Jxx Hamiltonian and Lagrangian systems
This subtopic studies Hamiltonian and Lagrangian systems, emphasizing conserved quantities, symplectic geometry, and the structure of mechanical and variational dynamics.
Specific topics
37J06 General theory of finite-dimensional Hamiltonian and Lagrangian systems
Overview
37J06 studies general theory of finite-dimensional hamiltonian and lagrangian systems within Hamiltonian and Lagrangian systems. The emphasis is on canonical formulations, invariant structures, and theorem frameworks that describe stability, complexity, and asymptotic behavior of trajectories or flows.
Related Wikipedia Page
Wikipedia search: General theory of finite-dimensional Hamiltonian and Lagrangian systems
Useful Links
Key Ideas
- Principal structures and model classes for general theory of finite-dimensional hamiltonian and lagrangian systems
- Invariant objects, long-time behavior, and stability or instability mechanisms
- Analytic, geometric, and probabilistic tools used to establish qualitative and quantitative results
Typical Uses
Used to identify dynamical regimes, choose proof techniques, and connect geometric, topological, and measure-theoretic perspectives when analyzing long-time evolution.
Applications
- Qualitative and quantitative modeling of nonlinear evolution phenomena
- Rigorous analysis of bifurcation, recurrence, transport, or asymptotic regimes
- Theoretical foundations for numerical simulation and data-informed dynamics workflows
References
Recommended Textbooks
37J11 Symplectic and canonical mappings
Overview
37J11 studies symplectic and canonical mappings within Hamiltonian and Lagrangian systems. The emphasis is on canonical formulations, invariant structures, and theorem frameworks that describe stability, complexity, and asymptotic behavior of trajectories or flows.
Related Wikipedia Page
Wikipedia search: Symplectic and canonical mappings
Useful Links
Key Ideas
- Principal structures and model classes for symplectic and canonical mappings
- Invariant objects, long-time behavior, and stability or instability mechanisms
- Analytic, geometric, and probabilistic tools used to establish qualitative and quantitative results
Typical Uses
Used to identify dynamical regimes, choose proof techniques, and connect geometric, topological, and measure-theoretic perspectives when analyzing long-time evolution.
Applications
- Qualitative and quantitative modeling of nonlinear evolution phenomena
- Rigorous analysis of bifurcation, recurrence, transport, or asymptotic regimes
- Theoretical foundations for numerical simulation and data-informed dynamics workflows
References
Recommended Textbooks
37J12 Fixed points and periodic points of Hamiltonian systems
Overview
37J12 studies fixed points and periodic points of hamiltonian systems within Hamiltonian and Lagrangian systems. The emphasis is on canonical formulations, invariant structures, and theorem frameworks that describe stability, complexity, and asymptotic behavior of trajectories or flows.
Related Wikipedia Page
Wikipedia search: Fixed points and periodic points of Hamiltonian systems
Useful Links
Key Ideas
- Principal structures and model classes for fixed points and periodic points of hamiltonian systems
- Invariant objects, long-time behavior, and stability or instability mechanisms
- Analytic, geometric, and probabilistic tools used to establish qualitative and quantitative results
Typical Uses
Used to identify dynamical regimes, choose proof techniques, and connect geometric, topological, and measure-theoretic perspectives when analyzing long-time evolution.
Applications
- Qualitative and quantitative modeling of nonlinear evolution phenomena
- Rigorous analysis of bifurcation, recurrence, transport, or asymptotic regimes
- Theoretical foundations for numerical simulation and data-informed dynamics workflows
References
Recommended Textbooks
37J25 Stability problems for finite-dimensional Hamiltonian and Lagrangian systems
Overview
37J25 studies stability problems for finite-dimensional hamiltonian and lagrangian systems within Hamiltonian and Lagrangian systems. The emphasis is on canonical formulations, invariant structures, and theorem frameworks that describe stability, complexity, and asymptotic behavior of trajectories or flows.
Related Wikipedia Page
Wikipedia search: Stability problems for finite-dimensional Hamiltonian and Lagrangian systems
Useful Links
Key Ideas
- Principal structures and model classes for stability problems for finite-dimensional hamiltonian and lagrangian systems
- Invariant objects, long-time behavior, and stability or instability mechanisms
- Analytic, geometric, and probabilistic tools used to establish qualitative and quantitative results
Typical Uses
Used to identify dynamical regimes, choose proof techniques, and connect geometric, topological, and measure-theoretic perspectives when analyzing long-time evolution.
Applications
- Qualitative and quantitative modeling of nonlinear evolution phenomena
- Rigorous analysis of bifurcation, recurrence, transport, or asymptotic regimes
- Theoretical foundations for numerical simulation and data-informed dynamics workflows
References
Recommended Textbooks
37J30 Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems
Overview
37J30 studies obstructions to integrability for finite-dimensional hamiltonian and lagrangian systems within Hamiltonian and Lagrangian systems. The emphasis is on canonical formulations, invariant structures, and theorem frameworks that describe stability, complexity, and asymptotic behavior of trajectories or flows.
Related Wikipedia Page
Wikipedia search: Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems
Useful Links
Key Ideas
- Principal structures and model classes for obstructions to integrability for finite-dimensional hamiltonian and lagrangian systems
- Invariant objects, long-time behavior, and stability or instability mechanisms
- Analytic, geometric, and probabilistic tools used to establish qualitative and quantitative results
Typical Uses
Used to identify dynamical regimes, choose proof techniques, and connect geometric, topological, and measure-theoretic perspectives when analyzing long-time evolution.
Applications
- Qualitative and quantitative modeling of nonlinear evolution phenomena
- Rigorous analysis of bifurcation, recurrence, transport, or asymptotic regimes
- Theoretical foundations for numerical simulation and data-informed dynamics workflows
References
Recommended Textbooks
37J35 Completely integrable finite-dimensional Hamiltonian systems
Overview
37J35 studies completely integrable finite-dimensional hamiltonian systems within Hamiltonian and Lagrangian systems. The emphasis is on canonical formulations, invariant structures, and theorem frameworks that describe stability, complexity, and asymptotic behavior of trajectories or flows.
Related Wikipedia Page
Wikipedia search: Completely integrable finite-dimensional Hamiltonian systems
Useful Links
Key Ideas
- Principal structures and model classes for completely integrable finite-dimensional hamiltonian systems
- Invariant objects, long-time behavior, and stability or instability mechanisms
- Analytic, geometric, and probabilistic tools used to establish qualitative and quantitative results
Typical Uses
Used to identify dynamical regimes, choose proof techniques, and connect geometric, topological, and measure-theoretic perspectives when analyzing long-time evolution.
Applications
- Qualitative and quantitative modeling of nonlinear evolution phenomena
- Rigorous analysis of bifurcation, recurrence, transport, or asymptotic regimes
- Theoretical foundations for numerical simulation and data-informed dynamics workflows
References
Recommended Textbooks
37J38 Lax pairs, Lax equations, and related concepts
Overview
37J38 studies lax pairs, lax equations, and related concepts within Hamiltonian and Lagrangian systems. The emphasis is on canonical formulations, invariant structures, and theorem frameworks that describe stability, complexity, and asymptotic behavior of trajectories or flows.
Related Wikipedia Page
Wikipedia search: Lax pairs, Lax equations, and related concepts
Useful Links
Key Ideas
- Principal structures and model classes for lax pairs, lax equations, and related concepts
- Invariant objects, long-time behavior, and stability or instability mechanisms
- Analytic, geometric, and probabilistic tools used to establish qualitative and quantitative results
Typical Uses
Used to identify dynamical regimes, choose proof techniques, and connect geometric, topological, and measure-theoretic perspectives when analyzing long-time evolution.
Applications
- Qualitative and quantitative modeling of nonlinear evolution phenomena
- Rigorous analysis of bifurcation, recurrence, transport, or asymptotic regimes
- Theoretical foundations for numerical simulation and data-informed dynamics workflows
References
Recommended Textbooks
37J39 Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and knot theory
Overview
37J39 studies relations of finite-dimensional hamiltonian and lagrangian systems with topology, geometry and knot theory within Hamiltonian and Lagrangian systems. The emphasis is on canonical formulations, invariant structures, and theorem frameworks that describe stability, complexity, and asymptotic behavior of trajectories or flows.
Related Wikipedia Page
Wikipedia search: Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and knot theory
Useful Links
Key Ideas
- Principal structures and model classes for relations of finite-dimensional hamiltonian and lagrangian systems with topology, geometry and knot theory
- Invariant objects, long-time behavior, and stability or instability mechanisms
- Analytic, geometric, and probabilistic tools used to establish qualitative and quantitative results
Typical Uses
Used to identify dynamical regimes, choose proof techniques, and connect geometric, topological, and measure-theoretic perspectives when analyzing long-time evolution.
Applications
- Qualitative and quantitative modeling of nonlinear evolution phenomena
- Rigorous analysis of bifurcation, recurrence, transport, or asymptotic regimes
- Theoretical foundations for numerical simulation and data-informed dynamics workflows
References
Recommended Textbooks
37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors
Overview
37J40 studies perturbations of finite-dimensional hamiltonian systems, normal forms, small divisors within Hamiltonian and Lagrangian systems. The emphasis is on canonical formulations, invariant structures, and theorem frameworks that describe stability, complexity, and asymptotic behavior of trajectories or flows.
Related Wikipedia Page
Wikipedia search: Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors
Useful Links
Key Ideas
- Principal structures and model classes for perturbations of finite-dimensional hamiltonian systems, normal forms, small divisors
- Invariant objects, long-time behavior, and stability or instability mechanisms
- Analytic, geometric, and probabilistic tools used to establish qualitative and quantitative results
Typical Uses
Used to identify dynamical regimes, choose proof techniques, and connect geometric, topological, and measure-theoretic perspectives when analyzing long-time evolution.
Applications
- Qualitative and quantitative modeling of nonlinear evolution phenomena
- Rigorous analysis of bifurcation, recurrence, transport, or asymptotic regimes
- Theoretical foundations for numerical simulation and data-informed dynamics workflows
References
Recommended Textbooks
37J45 Periodic, homoclinic and heteroclinic orbits of Hamiltonian systems
Overview
37J45 studies periodic, homoclinic and heteroclinic orbits of hamiltonian systems within Hamiltonian and Lagrangian systems. The emphasis is on canonical formulations, invariant structures, and theorem frameworks that describe stability, complexity, and asymptotic behavior of trajectories or flows.
Related Wikipedia Page
Wikipedia search: Periodic, homoclinic and heteroclinic orbits of Hamiltonian systems
Useful Links
Key Ideas
- Principal structures and model classes for periodic, homoclinic and heteroclinic orbits of hamiltonian systems
- Invariant objects, long-time behavior, and stability or instability mechanisms
- Analytic, geometric, and probabilistic tools used to establish qualitative and quantitative results
Typical Uses
Used to identify dynamical regimes, choose proof techniques, and connect geometric, topological, and measure-theoretic perspectives when analyzing long-time evolution.
Applications
- Qualitative and quantitative modeling of nonlinear evolution phenomena
- Rigorous analysis of bifurcation, recurrence, transport, or asymptotic regimes
- Theoretical foundations for numerical simulation and data-informed dynamics workflows
References
Recommended Textbooks
37J46 Periodic orbits of Hamiltonian systems
Overview
37J46 studies periodic orbits of hamiltonian systems within Hamiltonian and Lagrangian systems. The emphasis is on canonical formulations, invariant structures, and theorem frameworks that describe stability, complexity, and asymptotic behavior of trajectories or flows.
Related Wikipedia Page
Wikipedia search: Periodic orbits of Hamiltonian systems
Useful Links
Key Ideas
- Principal structures and model classes for periodic orbits of hamiltonian systems
- Invariant objects, long-time behavior, and stability or instability mechanisms
- Analytic, geometric, and probabilistic tools used to establish qualitative and quantitative results
Typical Uses
Used to identify dynamical regimes, choose proof techniques, and connect geometric, topological, and measure-theoretic perspectives when analyzing long-time evolution.
Applications
- Qualitative and quantitative modeling of nonlinear evolution phenomena
- Rigorous analysis of bifurcation, recurrence, transport, or asymptotic regimes
- Theoretical foundations for numerical simulation and data-informed dynamics workflows
References
Recommended Textbooks
37J51 Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; Mather theory
Overview
37J51 studies action-minimizing orbits and measures for finite-dimensional hamiltonian and lagrangian systems; mather theory within Hamiltonian and Lagrangian systems. The emphasis is on canonical formulations, invariant structures, and theorem frameworks that describe stability, complexity, and asymptotic behavior of trajectories or flows.
Related Wikipedia Page
Wikipedia search: Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; Mather theory
Useful Links
Key Ideas
- Principal structures and model classes for action-minimizing orbits and measures for finite-dimensional hamiltonian and lagrangian systems; mather theory
- Invariant objects, long-time behavior, and stability or instability mechanisms
- Analytic, geometric, and probabilistic tools used to establish qualitative and quantitative results
Typical Uses
Used to identify dynamical regimes, choose proof techniques, and connect geometric, topological, and measure-theoretic perspectives when analyzing long-time evolution.
Applications
- Qualitative and quantitative modeling of nonlinear evolution phenomena
- Rigorous analysis of bifurcation, recurrence, transport, or asymptotic regimes
- Theoretical foundations for numerical simulation and data-informed dynamics workflows
References
Recommended Textbooks
37J55 Contact systems
Overview
37J55 studies contact systems within Hamiltonian and Lagrangian systems. The emphasis is on canonical formulations, invariant structures, and theorem frameworks that describe stability, complexity, and asymptotic behavior of trajectories or flows.
Related Wikipedia Page
Wikipedia search: Contact systems
Useful Links
Key Ideas
- Principal structures and model classes for contact systems
- Invariant objects, long-time behavior, and stability or instability mechanisms
- Analytic, geometric, and probabilistic tools used to establish qualitative and quantitative results
Typical Uses
Used to identify dynamical regimes, choose proof techniques, and connect geometric, topological, and measure-theoretic perspectives when analyzing long-time evolution.
Applications
- Qualitative and quantitative modeling of nonlinear evolution phenomena
- Rigorous analysis of bifurcation, recurrence, transport, or asymptotic regimes
- Theoretical foundations for numerical simulation and data-informed dynamics workflows
References
Recommended Textbooks
37J65 Variational methods for infinite-dimensional Hamiltonian and Lagrangian systems
Overview
37J65 studies variational methods for infinite-dimensional hamiltonian and lagrangian systems within Hamiltonian and Lagrangian systems. The emphasis is on canonical formulations, invariant structures, and theorem frameworks that describe stability, complexity, and asymptotic behavior of trajectories or flows.
Related Wikipedia Page
Wikipedia search: Variational methods for infinite-dimensional Hamiltonian and Lagrangian systems
Useful Links
Key Ideas
- Principal structures and model classes for variational methods for infinite-dimensional hamiltonian and lagrangian systems
- Invariant objects, long-time behavior, and stability or instability mechanisms
- Analytic, geometric, and probabilistic tools used to establish qualitative and quantitative results
Typical Uses
Used to identify dynamical regimes, choose proof techniques, and connect geometric, topological, and measure-theoretic perspectives when analyzing long-time evolution.
Applications
- Qualitative and quantitative modeling of nonlinear evolution phenomena
- Rigorous analysis of bifurcation, recurrence, transport, or asymptotic regimes
- Theoretical foundations for numerical simulation and data-informed dynamics workflows
References
Recommended Textbooks
37J70 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems
Overview
37J70 studies completely integrable infinite-dimensional hamiltonian and lagrangian systems within Hamiltonian and Lagrangian systems. The emphasis is on canonical formulations, invariant structures, and theorem frameworks that describe stability, complexity, and asymptotic behavior of trajectories or flows.
Related Wikipedia Page
Wikipedia search: Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems
Useful Links
Key Ideas
- Principal structures and model classes for completely integrable infinite-dimensional hamiltonian and lagrangian systems
- Invariant objects, long-time behavior, and stability or instability mechanisms
- Analytic, geometric, and probabilistic tools used to establish qualitative and quantitative results
Typical Uses
Used to identify dynamical regimes, choose proof techniques, and connect geometric, topological, and measure-theoretic perspectives when analyzing long-time evolution.
Applications
- Qualitative and quantitative modeling of nonlinear evolution phenomena
- Rigorous analysis of bifurcation, recurrence, transport, or asymptotic regimes
- Theoretical foundations for numerical simulation and data-informed dynamics workflows
References
Recommended Textbooks
37J99 None of the above
Overview
37J99 studies none of the above within Hamiltonian and Lagrangian systems. The emphasis is on canonical formulations, invariant structures, and theorem frameworks that describe stability, complexity, and asymptotic behavior of trajectories or flows.
Related Wikipedia Page
Wikipedia search: None of the above
Useful Links
Key Ideas
- Principal structures and model classes for none of the above
- Invariant objects, long-time behavior, and stability or instability mechanisms
- Analytic, geometric, and probabilistic tools used to establish qualitative and quantitative results
Typical Uses
Used to identify dynamical regimes, choose proof techniques, and connect geometric, topological, and measure-theoretic perspectives when analyzing long-time evolution.
Applications
- Qualitative and quantitative modeling of nonlinear evolution phenomena
- Rigorous analysis of bifurcation, recurrence, transport, or asymptotic regimes
- Theoretical foundations for numerical simulation and data-informed dynamics workflows
References
Recommended Textbooks