INTRODUCTION TO DYNAMICS ON MODULI SPACES

Name: INTRODUCTION TO DYNAMICS ON MODULI SPACES
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MATH 858

과목 설명

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.

선수과목

Graduate/professional standing or declared in Mathematics VISP (graduate or dissertator)

충족 요건

This course does not satisfy any prerequisites.

학점

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개설 시기

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평점

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변화 계산 불가

수료율

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A 비율

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학급 규모

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과거 데이터 대비 변화 없음

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강사 (2026 Summr)

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유사 과목

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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.

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