Mathematics Branches, Topics, and Sub-Topics

A structured visual guide to the major mathematical areas and their relationships.

Search by code, branch, topic, subtopic, or a keyword from the descriptions.

37Nxx Applications to sciences

This subtopic studies applications of dynamical systems to the sciences, focusing on models from physics, biology, engineering, and other applied domains.

Specific topics

37N05 Dynamical systems in classical and celestial mechanics

Overview

37N05 studies dynamical systems in classical and celestial mechanics within applications to sciences. 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 in classical and celestial mechanics

Useful Links

Key Ideas

  • Core formulations and model classes for dynamical systems in classical and celestial mechanics
  • 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

37N10 Dynamical systems in fluid mechanics, oceanography and meteorology

Overview

37N10 studies dynamical systems in fluid mechanics, oceanography and meteorology within applications to sciences. 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 in fluid mechanics, oceanography and meteorology

Useful Links

Key Ideas

  • Core formulations and model classes for dynamical systems in fluid mechanics, oceanography and meteorology
  • 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

37N15 Dynamical systems in solid mechanics

Overview

37N15 studies dynamical systems in solid mechanics within applications to sciences. 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 in solid mechanics

Useful Links

Key Ideas

  • Core formulations and model classes for dynamical systems in solid mechanics
  • 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

37N20 Dynamical systems in other branches of physics

Overview

37N20 studies dynamical systems in other branches of physics within applications to sciences. 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 in other branches of physics

Useful Links

Key Ideas

  • Core formulations and model classes for dynamical systems in other branches of physics
  • 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

37N25 Dynamical systems in biology

Overview

37N25 studies dynamical systems in biology within applications to sciences. 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 in biology

Useful Links

Key Ideas

  • Core formulations and model classes for dynamical systems in biology
  • 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

37N30 Dynamical systems in numerical analysis

Overview

37N30 studies dynamical systems in numerical analysis within applications to sciences. 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 in numerical analysis

Useful Links

Key Ideas

  • Core formulations and model classes for dynamical systems in numerical analysis
  • 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

37N35 Dynamical systems in control

Overview

37N35 studies dynamical systems in control within applications to sciences. 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 in control

Useful Links

Key Ideas

  • Core formulations and model classes for dynamical systems in control
  • 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

37N40 Dynamical systems in optimization and economics

Overview

37N40 studies dynamical systems in optimization and economics within applications to sciences. 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 in optimization and economics

Useful Links

Key Ideas

  • Core formulations and model classes for dynamical systems in optimization and economics
  • 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