Survival of infinitely many critical points for the Rabinowitz action functional

TL;DR

This paper demonstrates that an infinite-dimensional Rabinowitz Floer homology guarantees infinitely many critical points of the Rabinowitz action functional, even in non-Morse cases, via filtered homology analysis.

Contribution

It establishes a link between infinite-dimensional Rabinowitz Floer homology and the existence of infinitely many critical points, extending previous results to non-Morse scenarios.

Findings

Infinite Rabinowitz Floer homology implies infinitely many critical points.

Critical points exist even when the functional is non-Morse.

Analysis uses filtered Rabinowitz Floer homology.

Abstract

In this paper, we show that if the Rabinowitz Floer homology has infinite dimension, there exist infinitely many critical points of a Rabinowitz action functional even though it could be non-Morse. This result is proved by examining the filtered Rabinowitz Floer homology.