On the Conley Conjecture for Reeb Flows

2014/07/07 by Ginzburg, Viktor L., Gurel, Basak Z., Macarini, Leonardo · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1407.1773

Abstract

In this paper we prove the existence of infinitely many closed Reeb orbits for a certain class of contact manifolds. This result can be viewed as a contact analogue of the Hamiltonian Conley conjecture. The manifolds for which the contact Conley conjecture is established are the pre-quantization circle bundles with aspherical base. As an application, we prove that for a surface of genus at least two with a non-vanishing magnetic field, the twisted geodesic flow has infinitely many periodic orbits on every low energy level.

Cited by

• The growth rate of closed prime magnetic geodesics on closed contact manifolds

Related

• The Conley Conjecture and Beyond
• Closed Reeb orbits on the sphere and symplectically degenerate maxima
• Proof of Hofer-Wysocki-Zehnder's two or infinity conjecture
• On the existence of infinitely many invariant Reeb orbits
• Dynamical convexity and elliptic periodic orbits for Reeb flows