Variational destruction of invariant circles

2011/06/30 by Lin Wang, Wang, Lin · 2 citations
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1106.6137

openalex publication_date 2011/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a sequence of generating functions (h_n)_n∈\N, arbitrarily close to an integrable system in the C^r topology with r<4 for n large enough. With the variational method, we prove that for a given rotation number ω and n large enough, the exact monotone area-preserving twist maps generated by (h_n)_n∈\N admit no invariant circles with rotation number ω.

Cited by

• Herman's converse KAM mechanism revisited
• On the Dynamics of Invariant Graphs for Dissipative Twist Maps

Related

• Quantitative destruction of invariant circles
• On Non-KAM Invariant Circles for Area-Preserving Twist Maps
• Variational structures for infinite transition orbits of monotone twist maps
• Regularity properties of critical invariant circles of twist maps, and their universality
• Moser's twist theorem revisited