# Corrigendum: The Conley conjecture for Hamiltonian systems on the cotangent bundle and its analogue for Lagrangian systems - Mathematics > Symplectic Geometry

Corrigendum: The Conley conjecture for Hamiltonian systems on the cotangent bundle and its analogue for Lagrangian systems - Mathematics > Symplectic Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: In lines 8-11 of \citepp. 2977{Lu} we wrote: -For integer $m\ge 3$, if $M$is $C^m$-smooth and$C^{m-1}$-smooth $L:\R\times TM\to\R$ satisfies the assumptions L1-L3,then the functional ${\cal L} \tau$ is $C^2$-smooth, bounded below, satisfiesthe Palais-Smale condition, and all critical points of it have finite Morseindexes and nullities see \citeProp.4.1, 4.2{AbF} and \cite{Be}.- However,as proved in \cite{AbSc1} the claim that ${\cal L} \tau$ is $C^2$-smooth istrue if and only if for every $t,q$ the function $v\mapsto Lt,q,v$ is apolynomial of degree at most 2. So the arguments in \cite{Lu} is only valid forthe physical Hamiltonian in 1.2 and corresponding Lagrangian therein. In thisnote we shall correct our arguments in \cite{Lu} with a new splitting lemmaobtained in \cite{Lu2}.

Author: ** Guangcun Lu**

Source: https://arxiv.org/