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arXiv · 1509.05325

Robust cycles and tangencies of large codimension

Pablo G. Barrientos·Artem Raibekas
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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 $d\geq 4$. 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.

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Pablo G. Barrientos, Artem Raibekas. 2017-07-21. Robust cycles and tangencies of large codimension. https://arxiv.org/abs/1509.05325

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