Robust cycles and tangencies of large codimension

2015/09/17 by Pablo G. Barrientos, Barrientos, Pablo G., Artem Raibekas +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1509.05325

openalex publication_date 2015/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct partially hyperbolic diffeomorphisms having semi-local robustly transitive sets with C¹-robust cycles of any co-index. These constructions also provide a new method to create C²-robust homoclinic, equidimensional and heterodimensional tangencies of large codimension in dimension d≥ 4. The method to generate robust homoclinic and equidimensional tangencies also works in the symplectic setting. Thus, these are mechanisms for the robust non-hyperbolicity of symplectomorphisms in higher dimension.

Citations

• Steps towards a classification of C^r-generic dynamics close to homoclinic points
• Extremal Lyapunov exponents: an invariance principle and applications
• On category, in the sense of Lusternik-Schnirelmann

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• Homoclinic tangencies leading to robust heterodimensional cycles
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• Robust complex heterodimensional cycles