Invariant probability measures from pseudoholomorphic curves Ⅰ
Copyright policy )Invariant probability measures from pseudoholomorphic curves Ⅰ
We introduce a method for constructing invariant probability measures of a large class of non-singular volume-preserving flows on closed, oriented odd-dimensional smooth manifolds using pseudoholomorphic curve techniques from symplectic geometry. These flows include any non-singular volume preserving flow in dimension three, and autonomous Hamiltonian flows on closed, regular energy levels in symplectic manifolds of any dimension. As an application, we use our method to prove the existence of obstructions to unique ergodicity for this class of flows, generalizing results of Taubes and Ginzburg-Niche.
55 pages, 2 figures. v2: Replaced an application (Proposition 1.10) of the main results with a slightly weaker version due to an error in its proof. Minor language/typo cleanup. Submitted
invariant measures, holomorphic curves, Symplectic field theory; contact homology, Ergodicity, mixing, rates of mixing, unique ergodicity, Dynamical Systems (math.DS), Hamiltonian flows, Mathematics - Symplectic Geometry, Pseudoholomorphic curves, Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, FOS: Mathematics, Contact manifolds (general theory), Symplectic Geometry (math.SG), Mathematics - Dynamical Systems
invariant measures, holomorphic curves, Symplectic field theory; contact homology, Ergodicity, mixing, rates of mixing, unique ergodicity, Dynamical Systems (math.DS), Hamiltonian flows, Mathematics - Symplectic Geometry, Pseudoholomorphic curves, Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, FOS: Mathematics, Contact manifolds (general theory), Symplectic Geometry (math.SG), Mathematics - Dynamical Systems
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