Non-integrability of open billiard flows and Dolgopyat-type estimates
For an open billiard flow in \(\mathbb R^n\), the author shows that the standard symplectic form \(d\alpha\) in \(\mathbb R^n\) satisfies a specific non-integrability condition over its non-wandering set \(\Lambda\). This together with the author's other new results provide Dolgopyat-type estimates for the spectra of Ruelle transfer operators under simpler conditions. The author also describes a class of open billiard flows in \(\mathbb R^n\), \(n\geq 3\), satisfying a certain pinching condition, which in turn implies that the (un)stable laminations over the non-wandering set are \(C^1\).
scientific article; zbMATH DE number 6038238
scientific article