Conley Conjecture for Negative Monotone Symplectic Manifolds

TL;DR

This paper proves that Hamiltonian diffeomorphisms on negative monotone closed symplectic manifolds have infinitely many periodic orbits, confirming the Conley conjecture in this setting.

Contribution

It establishes the Conley conjecture for negative monotone symplectic manifolds, a case previously unresolved in symplectic topology.

Findings

Existence of infinitely many periodic orbits for Hamiltonian diffeomorphisms on negative monotone manifolds

Extension of the Conley conjecture to a new class of symplectic manifolds

Advancement in understanding Hamiltonian dynamics in symplectic topology

Abstract

We prove the Conley conjecture for negative monotone, closed symplectic manifolds, i.e., the existence of infinitely many periodic orbits for Hamiltonian diffeomorphisms of such manifolds.