37Pxx Arithmetic and non-Archimedean dynamics
This subtopic studies arithmetic and non-Archimedean dynamics, where iteration, periodic points, and stability are analyzed over number-theoretic or ultrametric fields.
Specific topics
37P05 Arithmetic and non-Archimedean dynamical systems involving polynomial maps of one variable
Overview
37P05 studies arithmetic and non-archimedean dynamical systems involving polynomial maps of one variable within arithmetic and non-Archimedean dynamics. Emphasis is placed on canonical models, principal estimates, and theorem patterns that explain existence, regularity, stability, and asymptotic dynamics.
Related Wikipedia Page
Wikipedia search: Arithmetic and non-Archimedean dynamical systems involving polynomial maps of one variable
Useful Links
Key Ideas
- Core formulations and model classes for arithmetic and non-archimedean dynamical systems involving polynomial maps of one variable
- Invariant structures, stability, and long-time behavior in discrete or continuous-time settings
- Analytical and computational techniques used for qualitative and quantitative results
Typical Uses
Used to classify problem regimes, select suitable proof techniques, and connect theoretical insight with computational or application-focused modeling pipelines.
Applications
- Modeling nonlinear evolution processes in mathematics and applied sciences
- Rigorous analysis of stability, recurrence, and asymptotic regimes
- Numerical simulation workflows guided by provable structural properties
References
Recommended Textbooks
37P10 Families and moduli spaces in arithmetic and non-Archimedean dynamics
Overview
37P10 studies families and moduli spaces in arithmetic and non-archimedean dynamics within arithmetic and non-Archimedean dynamics. Emphasis is placed on canonical models, principal estimates, and theorem patterns that explain existence, regularity, stability, and asymptotic dynamics.
Related Wikipedia Page
Wikipedia search: Families and moduli spaces in arithmetic and non-Archimedean dynamics
Useful Links
Key Ideas
- Core formulations and model classes for families and moduli spaces in arithmetic and non-archimedean dynamics
- Invariant structures, stability, and long-time behavior in discrete or continuous-time settings
- Analytical and computational techniques used for qualitative and quantitative results
Typical Uses
Used to classify problem regimes, select suitable proof techniques, and connect theoretical insight with computational or application-focused modeling pipelines.
Applications
- Modeling nonlinear evolution processes in mathematics and applied sciences
- Rigorous analysis of stability, recurrence, and asymptotic regimes
- Numerical simulation workflows guided by provable structural properties
References
Recommended Textbooks
37P15 Global ground fields in arithmetic dynamics
Overview
37P15 studies global ground fields in arithmetic dynamics within arithmetic and non-Archimedean dynamics. Emphasis is placed on canonical models, principal estimates, and theorem patterns that explain existence, regularity, stability, and asymptotic dynamics.
Related Wikipedia Page
Wikipedia search: Global ground fields in arithmetic dynamics
Useful Links
Key Ideas
- Core formulations and model classes for global ground fields in arithmetic dynamics
- Invariant structures, stability, and long-time behavior in discrete or continuous-time settings
- Analytical and computational techniques used for qualitative and quantitative results
Typical Uses
Used to classify problem regimes, select suitable proof techniques, and connect theoretical insight with computational or application-focused modeling pipelines.
Applications
- Modeling nonlinear evolution processes in mathematics and applied sciences
- Rigorous analysis of stability, recurrence, and asymptotic regimes
- Numerical simulation workflows guided by provable structural properties
References
Recommended Textbooks
37P20 Non-Archimedean local and global ground fields in arithmetic dynamics
Overview
37P20 studies non-archimedean local and global ground fields in arithmetic dynamics within arithmetic and non-Archimedean dynamics. Emphasis is placed on canonical models, principal estimates, and theorem patterns that explain existence, regularity, stability, and asymptotic dynamics.
Related Wikipedia Page
Wikipedia search: Non-Archimedean local and global ground fields in arithmetic dynamics
Useful Links
Key Ideas
- Core formulations and model classes for non-archimedean local and global ground fields in arithmetic dynamics
- Invariant structures, stability, and long-time behavior in discrete or continuous-time settings
- Analytical and computational techniques used for qualitative and quantitative results
Typical Uses
Used to classify problem regimes, select suitable proof techniques, and connect theoretical insight with computational or application-focused modeling pipelines.
Applications
- Modeling nonlinear evolution processes in mathematics and applied sciences
- Rigorous analysis of stability, recurrence, and asymptotic regimes
- Numerical simulation workflows guided by provable structural properties
References
Recommended Textbooks
37P25 Arithmetic properties of periodic points
Overview
37P25 studies arithmetic properties of periodic points within arithmetic and non-Archimedean dynamics. Emphasis is placed on canonical models, principal estimates, and theorem patterns that explain existence, regularity, stability, and asymptotic dynamics.
Related Wikipedia Page
Wikipedia search: Arithmetic properties of periodic points
Useful Links
Key Ideas
- Core formulations and model classes for arithmetic properties of periodic points
- Invariant structures, stability, and long-time behavior in discrete or continuous-time settings
- Analytical and computational techniques used for qualitative and quantitative results
Typical Uses
Used to classify problem regimes, select suitable proof techniques, and connect theoretical insight with computational or application-focused modeling pipelines.
Applications
- Modeling nonlinear evolution processes in mathematics and applied sciences
- Rigorous analysis of stability, recurrence, and asymptotic regimes
- Numerical simulation workflows guided by provable structural properties
References
Recommended Textbooks
37P30 Height functions in arithmetic dynamics
Overview
37P30 studies height functions in arithmetic dynamics within arithmetic and non-Archimedean dynamics. Emphasis is placed on canonical models, principal estimates, and theorem patterns that explain existence, regularity, stability, and asymptotic dynamics.
Related Wikipedia Page
Wikipedia search: Height functions in arithmetic dynamics
Useful Links
Key Ideas
- Core formulations and model classes for height functions in arithmetic dynamics
- Invariant structures, stability, and long-time behavior in discrete or continuous-time settings
- Analytical and computational techniques used for qualitative and quantitative results
Typical Uses
Used to classify problem regimes, select suitable proof techniques, and connect theoretical insight with computational or application-focused modeling pipelines.
Applications
- Modeling nonlinear evolution processes in mathematics and applied sciences
- Rigorous analysis of stability, recurrence, and asymptotic regimes
- Numerical simulation workflows guided by provable structural properties
References
Recommended Textbooks
37P35 Arithmetic properties of preperiodic points
Overview
37P35 studies arithmetic properties of preperiodic points within arithmetic and non-Archimedean dynamics. Emphasis is placed on canonical models, principal estimates, and theorem patterns that explain existence, regularity, stability, and asymptotic dynamics.
Related Wikipedia Page
Wikipedia search: Arithmetic properties of preperiodic points
Useful Links
Key Ideas
- Core formulations and model classes for arithmetic properties of preperiodic points
- Invariant structures, stability, and long-time behavior in discrete or continuous-time settings
- Analytical and computational techniques used for qualitative and quantitative results
Typical Uses
Used to classify problem regimes, select suitable proof techniques, and connect theoretical insight with computational or application-focused modeling pipelines.
Applications
- Modeling nonlinear evolution processes in mathematics and applied sciences
- Rigorous analysis of stability, recurrence, and asymptotic regimes
- Numerical simulation workflows guided by provable structural properties
References
Recommended Textbooks
37P40 Non-Archimedean Fatou and Julia sets
Overview
37P40 studies non-archimedean fatou and julia sets within arithmetic and non-Archimedean dynamics. Emphasis is placed on canonical models, principal estimates, and theorem patterns that explain existence, regularity, stability, and asymptotic dynamics.
Related Wikipedia Page
Wikipedia search: Non-Archimedean Fatou and Julia sets
Useful Links
Key Ideas
- Core formulations and model classes for non-archimedean fatou and julia sets
- Invariant structures, stability, and long-time behavior in discrete or continuous-time settings
- Analytical and computational techniques used for qualitative and quantitative results
Typical Uses
Used to classify problem regimes, select suitable proof techniques, and connect theoretical insight with computational or application-focused modeling pipelines.
Applications
- Modeling nonlinear evolution processes in mathematics and applied sciences
- Rigorous analysis of stability, recurrence, and asymptotic regimes
- Numerical simulation workflows guided by provable structural properties
References
Recommended Textbooks
37P45 Families and moduli spaces in non-Archimedean dynamics
Overview
37P45 studies families and moduli spaces in non-archimedean dynamics within arithmetic and non-Archimedean dynamics. Emphasis is placed on canonical models, principal estimates, and theorem patterns that explain existence, regularity, stability, and asymptotic dynamics.
Related Wikipedia Page
Wikipedia search: Families and moduli spaces in non-Archimedean dynamics
Useful Links
Key Ideas
- Core formulations and model classes for families and moduli spaces in non-archimedean dynamics
- Invariant structures, stability, and long-time behavior in discrete or continuous-time settings
- Analytical and computational techniques used for qualitative and quantitative results
Typical Uses
Used to classify problem regimes, select suitable proof techniques, and connect theoretical insight with computational or application-focused modeling pipelines.
Applications
- Modeling nonlinear evolution processes in mathematics and applied sciences
- Rigorous analysis of stability, recurrence, and asymptotic regimes
- Numerical simulation workflows guided by provable structural properties
References
Recommended Textbooks
37P50 Dynamical systems on Berkovich spaces
Overview
37P50 studies dynamical systems on berkovich spaces within arithmetic and non-Archimedean dynamics. Emphasis is placed on canonical models, principal estimates, and theorem patterns that explain existence, regularity, stability, and asymptotic dynamics.
Related Wikipedia Page
Wikipedia search: Dynamical systems on Berkovich spaces
Useful Links
Key Ideas
- Core formulations and model classes for dynamical systems on berkovich spaces
- Invariant structures, stability, and long-time behavior in discrete or continuous-time settings
- Analytical and computational techniques used for qualitative and quantitative results
Typical Uses
Used to classify problem regimes, select suitable proof techniques, and connect theoretical insight with computational or application-focused modeling pipelines.
Applications
- Modeling nonlinear evolution processes in mathematics and applied sciences
- Rigorous analysis of stability, recurrence, and asymptotic regimes
- Numerical simulation workflows guided by provable structural properties
References
Recommended Textbooks
37P55 Arithmetic dynamics on general algebraic varieties
Overview
37P55 studies arithmetic dynamics on general algebraic varieties within arithmetic and non-Archimedean dynamics. Emphasis is placed on canonical models, principal estimates, and theorem patterns that explain existence, regularity, stability, and asymptotic dynamics.
Related Wikipedia Page
Wikipedia search: Arithmetic dynamics on general algebraic varieties
Useful Links
Key Ideas
- Core formulations and model classes for arithmetic dynamics on general algebraic varieties
- Invariant structures, stability, and long-time behavior in discrete or continuous-time settings
- Analytical and computational techniques used for qualitative and quantitative results
Typical Uses
Used to classify problem regimes, select suitable proof techniques, and connect theoretical insight with computational or application-focused modeling pipelines.
Applications
- Modeling nonlinear evolution processes in mathematics and applied sciences
- Rigorous analysis of stability, recurrence, and asymptotic regimes
- Numerical simulation workflows guided by provable structural properties
References
Recommended Textbooks
37P99 None of the above
Overview
37P99 studies none of the above within arithmetic and non-Archimedean dynamics. Emphasis is placed on canonical models, principal estimates, and theorem patterns that explain existence, regularity, stability, and asymptotic dynamics.
Related Wikipedia Page
Wikipedia search: None of the above
Useful Links
Key Ideas
- Core formulations and model classes for none of the above
- Invariant structures, stability, and long-time behavior in discrete or continuous-time settings
- Analytical and computational techniques used for qualitative and quantitative results
Typical Uses
Used to classify problem regimes, select suitable proof techniques, and connect theoretical insight with computational or application-focused modeling pipelines.
Applications
- Modeling nonlinear evolution processes in mathematics and applied sciences
- Rigorous analysis of stability, recurrence, and asymptotic regimes
- Numerical simulation workflows guided by provable structural properties
References
Recommended Textbooks