Invariant probability measures from pseudoholomorphic curves I
Abstract
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.
Cite
@article{arxiv.2109.00102,
title = {Invariant probability measures from pseudoholomorphic curves I},
author = {Rohil Prasad},
journal= {arXiv preprint arXiv:2109.00102},
year = {2021}
}
Comments
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