Bifurcations for Lagrangian systems and geodesics

2024/04/29 by Lu, Guangcun
#34C23 #37J20 #58E05 #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2404.18815

Abstract

In this paper we shall use the abstract bifurcation theorems developed by the author in previous papers to study bifurcations of solutions for Lagrangian systems on manifolds linearly or nonlinearly dependent on parameters under various boundary value conditions. As applications, many bifurcation results for geodesics on Finsler and Riemannian manifolds are derived.

Related

• Comparative analysis for pair of dynamical systems, one of which is Lagrangian
• Dynamical stability in Lagrangian systems
• Global bifurcation techniques for Yamabe type equations on Riemannian manifolds
• Variational principle for bifurcation in Lagrangian mechanics
• Lagrangian systems on hyperbolic manifolds