8 papers
Existence of a positive hyperbolic orbit in three-dimensional Reeb flows
Taisuke Shibata
Non-degenerate periodic orbits in three-dimensional Reeb flows are classified into three types: positive hyperbolic, negative hyperbolic and elliptic. In the present paper, we cons…
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…
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^{…
Area-preserving diffeomorphisms on the disk and positive hyperbolic orbits
Masayuki Asaoka, Taisuke Shibata
In this paper, we prove that if an area-preserving non-degenerate diffeomorphism on the open disk which extend smoothly to the boundary with non-degeneracy has at least 2 interior…
Dynamically convex and global surface of section in from the viewpoint of ECH
Taisuke Shibata
The notion of dynamically convex has been studied since it was introduced by Hofer, Wysocki and Zehnder. In particular, they showed that there muse exist a global surface of sectio…
The Conley-Zehnder index of a minimal orbit and existence of a positive hyperbolic orbit
Taisuke Shibata
As a refinement of the Weinstein conjecture, it is a natural question whether a Reeb orbit of particular types exists. D. Cristofaro-Gardiner, M. Hutchings and D. Pomerleano showed…
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…
Existence of a positive hyperbolic Reeb orbit in three spheres with finite free group actions
Taisuke Shibata
Let be a non-degenerate contact three manifold. D. Cristfaro-Gardiner, M. Hutshings and D. Pomerleano showed that if is torsion, then the Reeb vect…