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DYNAMICAL SYSTEMS

MATH 807
과목 설명

Treats the qualitative behavior of continuous and discrete dynamical systems, including Hamiltonian systems of differential equations. Typical topics include periodic and almost periodic solutions, the fixed point theorem of Poincare and Birkhoff, invariant curves and KAM theory, celestial mechanics, and chaotic behavior.

선수과목

Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

충족 요건

This course does not satisfy any prerequisites.

학점

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평점
3.93

9.87% 과거 데이터 대비

수료율
100%

3.13% 과거 데이터 대비

A 비율
85.71%

28.57% 과거 데이터 대비

학급 규모
14

27.27% 과거 데이터 대비

Cumulative Grade Distribution

강사 (2026 Summr)

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유사 과목

APPLIED DYNAMICAL SYSTEMS, CHAOS AND MODELING

MATH 415

An introduction to nonlinear dynamical systems including stability, bifurcations and chaos. The course will give underlying mathematical ideas, but emphasize applications from many scientific fields.

INTRODUCTION TO ERGODIC THEORY AND DYNAMICS

MATH 758

An introduction to ergodic theory and dynamics covering fundamental theorems of ergodic theory, classical examples of one and two dimensional dynamics as well as applications to study of group actions.

ORDINARY DIFFERENTIAL EQUATIONS

MATH 716

Existence, uniqueness, and continuous dependence theorems, linear systems, stability, singular points, and boundary value problems. Qualitative behavior of nonlinear equations, stability, Lyapunov functions, invariant manifolds, bifurcation theory, periodic orbits, and connecting orbits.

ORDINARY DIFFERENTIAL EQUATIONS

MATH 519

Provides a rigorous introduction to ordinary differential equations and dynamical systems. Intended for math majors and advanced (or graduate) students in other disciplines.

INTRODUCTION TO DYNAMICS ON MODULI SPACES

MATH 858

An introduction to ergodic theory and dynamics on the moduli space of translation surfaces with applications to counting problems in rational billiards and on flat surfaces. Covers dynamical techniques inspired by homogeneous dynamics including the use of Margulis functions to establish quantitative recurrence results; the use of random walks, inspired by work of Benoist and Quint, to prove measure rigidity statements; and the use of Zimmer's theory of the algebraic hull to prove finiteness results.