Robust cycles and tangencies of large codimension

Abstract

We construct partially hyperbolic diffeomorphisms having semi-local robustly transitive sets with $C^1$-robust cycles of any co-index. These constructions also provide a new method to create $C^2$-robust homoclinic, equidimensional and heterodimensional tangencies of large codimension in dimension $d\ge 4$. 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.

This article has been divided into two parts: arXiv:1509.05325 and arXiv:1707.06473

References in corpus (2)

• On the geometry of horseshoes in higher dimensions
• Steps towards a classification of $C^r$-generic dynamics close to homoclinic points

Cited by in corpus (3)

• Non-trivial wandering domains for heterodimensional cycles
• A link between Topological Entropy and Lyapunov Exponents
• Typical coexistence of infinitely many strange attractors