3 papers
math.DS2026
Positive hyperbolic periodic orbits for area-preserving maps and Reeb flows
Masayuki Asaoka, Taisuke Shibata
We prove that a strongly nondegenerate Reeb vector field on a closed contact three-manifold has infinitely many simple positive hyperbolic periodic orbits if it has at least three…
math.SG2023
Elliptic bindings and the first ECH spectrum for convex Reeb flows on lens spaces
Taisuke Shibata
In this paper, at first we introduce a sufficient condition for a rational unknotted Reeb orbit in a lens space to be elliptic by using the rational self-linking number $sl_ξ^{…
math.SG2022
Existence of a positive hyperbolic orbit in the presence of an elliptic orbit in three-dimensional Reeb flows
Taisuke Shibata
Nondegenerate periodic orbits in three-dimensional Reeb flows can be classified into three types, positive hyperbolic, negative hyperbolic and elliptic. As a problem which involves…