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Title: Symplectic dynamics: Invariant measures, closing lemmas, and equidistribution
Authors: Prasad, Rohil
Advisors: Hofer, Helmut
Contributors: Mathematics Department
Subjects: Mathematics
Issue Date: 2023
Publisher: Princeton, NJ : Princeton University
Abstract: In this thesis, we develop and apply techniques in symplectic geometry and gauge theory to study symplectic dynamical systems. The first part devises a method to construct invariant measures of Hamiltonian flows from pseudoholomorphic curves, and applies it to show broad classes of these systems are not uniquely ergodic. The second part studies quantitative invariants from Periodic Floer homology, in particular using Seiberg–Witten theory to give a precise accounting of their high-degree asymptotics. The main dynamical application is a proof that a generic area-preserving diffeomorphism of a compact surface has an equidistributed sequence of periodic orbits.
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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