The Rabinowitz minimal periodic solution conjecture on partially convex reversible Hamiltonian systems and brake subharmonics

2025/09/29 by Zhou, Yuting
#34C25 #37J99 #53D12 #58E05 #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2509.25567

Abstract

Under weaker regularity and compactness assumptions, we find the mountain-pass essential point, which is a novel extension of the classical Ambrosetti-Rabinowitz mountain pass theorem. We study the reversible superquadratic autonomous Hamiltonian systems whose Hamiltonian H(p,q) is strictly convex in the position q\inRⁿ and prove that for every T>0, the system has a T-periodic brake solution x with minimal period T, provided the Hessian H_pp( x(t))\inR^{n× n} is semi-positive definite for t\inR or n=1. For brake subharmonics of general reversible nonautonomous Hamiltonian systems, we also get some new results.

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