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arXiv · 2501.07950

Robust complex heterodimensional cycles

Sébastien Biebler
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Abstract

A diffeomorphism f has a heterodimensional cycle if it displays two (transitive) hyperbolic sets K and K' with different indices such that the unstable set of K intersects the stable one of K' and vice versa. We prove that it is possible to find robust heterodimensional cycles for families of polynomial automorphisms of C^3 . The proof is based on Bonatti-D{\'i}az blenders.

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Sébastien Biebler. 2025-01-14. Robust complex heterodimensional cycles. https://arxiv.org/abs/2501.07950

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