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arXiv · 1806.06409

H\'enon-like families and blender-horseshoes at non-transverse heterodimensional cycles

Lorenzo J. Díaz·Sebastián A. Pérez
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Abstract

In dimension three and under certain regularity assumptions, we construct a renormalisation scheme at the heterodimensional tangency of a non-transverse heterodimensional cycle associated with a pair of saddle-foci whose limit dynamic is a center-unstable H\'enon-like family displaying blender-horseshoes. As a consequence, the initial cycle can be approximated in higher regularity topologies by diffeomorphisms having blender-horseshoes.

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Lorenzo J. Díaz, Sebastián A. Pérez. 2018-06-17. H\'enon-like families and blender-horseshoes at non-transverse heterodimensional cycles. https://doi.org/10.1142/s0218127419300064

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