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arXiv · 1304.3965

Blenders in center unstable Hénon-like families: with an application to heterodimensional bifurcations

Lorenzo J. Díaz·Shin Kiriki·Katsutoshi Shinohara
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Abstract

We give an explicit family of polynomial maps called center unstable Hénon-like maps and prove that they exhibits blenders for some parametervalues. Using this family, we also prove the occurrence of blenders near certain non-transverse heterodimensional cycles under high regularity assumptions. The proof involves a renormalization scheme along heteroclinic orbits. We also investigate the connection between the blender and the original heterodimensional cycle.

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Lorenzo J. Díaz, Shin Kiriki, Katsutoshi Shinohara. 2013-04-15. Blenders in center unstable Hénon-like families: with an application to heterodimensional bifurcations. https://doi.org/10.1088/0951-7715%2F27%2F3%2F353

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