37Kxx Infinite-dimensional systems
This subtopic studies infinite-dimensional systems, including PDE-based or operator-theoretic models whose phase spaces have infinitely many degrees of freedom.
Specific topics
37K06 General theory of infinite-dimensional Hamiltonian and Lagrangian systems
Overview
37K06 studies general theory of infinite-dimensional hamiltonian and lagrangian systems within infinite-dimensional 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 infinite-dimensional Hamiltonian and Lagrangian systems
Useful Links
Key Ideas
- Principal structures and model classes for general theory of 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
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems
Overview
37K10 studies completely integrable infinite-dimensional hamiltonian and lagrangian systems within infinite-dimensional 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
37K15 Integration of completely integrable systems by inverse spectral and scattering methods
Overview
37K15 studies integration of completely integrable systems by inverse spectral and scattering methods within infinite-dimensional 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: Integration of completely integrable systems by inverse spectral and scattering methods
Useful Links
Key Ideas
- Principal structures and model classes for integration of completely integrable systems by inverse spectral and scattering methods
- 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
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry
Overview
37K20 studies relations of infinite-dimensional hamiltonian and lagrangian dynamical systems with algebraic geometry within infinite-dimensional 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 infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry
Useful Links
Key Ideas
- Principal structures and model classes for relations of infinite-dimensional hamiltonian and lagrangian dynamical systems with algebraic geometry
- 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
37K25 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology
Overview
37K25 studies relations of infinite-dimensional hamiltonian and lagrangian dynamical systems with topology within infinite-dimensional 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 infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology
Useful Links
Key Ideas
- Principal structures and model classes for relations of infinite-dimensional hamiltonian and lagrangian dynamical systems with topology
- 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
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras
Overview
37K30 studies relations of infinite-dimensional hamiltonian and lagrangian dynamical systems with infinite-dimensional lie algebras within infinite-dimensional 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 infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras
Useful Links
Key Ideas
- Principal structures and model classes for relations of infinite-dimensional hamiltonian and lagrangian dynamical systems with infinite-dimensional lie algebras
- 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
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
Overview
37K35 studies lie-bã¤cklund and other transformations for infinite-dimensional hamiltonian and lagrangian systems within infinite-dimensional 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: Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
Useful Links
Key Ideas
- Principal structures and model classes for lie-bã¤cklund and other transformations 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
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
Overview
37K40 studies soliton theory, asymptotic behavior of solutions of infinite-dimensional hamiltonian systems within infinite-dimensional 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: Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
Useful Links
Key Ideas
- Principal structures and model classes for soliton theory, asymptotic behavior of solutions of infinite-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
37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems
Overview
37K45 studies stability problems for infinite-dimensional hamiltonian and lagrangian systems within infinite-dimensional 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 infinite-dimensional Hamiltonian and Lagrangian systems
Useful Links
Key Ideas
- Principal structures and model classes for stability problems 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
37K50 Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems
Overview
37K50 studies bifurcation problems for infinite-dimensional hamiltonian and lagrangian systems within infinite-dimensional 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: Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems
Useful Links
Key Ideas
- Principal structures and model classes for bifurcation problems 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
37K55 Perturbations, KAM for infinite-dimensional Hamiltonian and Lagrangian systems
Overview
37K55 studies perturbations, kam for infinite-dimensional hamiltonian and lagrangian systems within infinite-dimensional 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, KAM for infinite-dimensional Hamiltonian and Lagrangian systems
Useful Links
Key Ideas
- Principal structures and model classes for perturbations, kam 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
37K58 Variational methods for infinite-dimensional Hamiltonian and Lagrangian systems
Overview
37K58 studies variational methods for infinite-dimensional hamiltonian and lagrangian systems within infinite-dimensional 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
37K60 Lattice dynamics and infinite-dimensional systems
Overview
37K60 studies lattice dynamics and infinite-dimensional systems within infinite-dimensional 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: Lattice dynamics and infinite-dimensional systems
Useful Links
Key Ideas
- Principal structures and model classes for lattice dynamics and infinite-dimensional 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