Periodic solutions of autonomous S¹-symmetric Newtonian systems

2025/10/17 by Anna Gołȩbiewska, Golebiewska, A., Sławomir Rybicki +3 · 1 citation
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2510.16073

openalex publication_date 2025/10/17 · openalex created_date 2025/10/22 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to formulate necessary conditions and sufficient ones for the existence of closed connected sets of nonstationary 2 π-periodic solutions of S¹-symmetric Newtonian systems in C_{2 π}([0,2π],Ω) × (0,+ ∞). As the main topological tool we apply the degree for equivariant gradient maps.

Citations

• Symmetric Liapunov center theorem for minimal orbit

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• Global bifurcation of solutions to elliptic systems with system and domain symmetries

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