On existence of expanding attractors with different dimensions

2024/05/23 by Medvedev, V., Zhuzhoma, E.
#37D15 #57R50 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.14196

Abstract

We prove that n-sphere \mathbbSⁿ, n≥ 2, admits structurally stable diffeomorphisms \mathbbSⁿ→\mathbbSⁿ with non-orientable expanding attractors of any topological dimension d∈\1,…,[(n)/(2)]\ where [x] is an integer part of x. One proves that n-torus \mathbbTⁿ, n≥ 2, admits structurally stable diffeomorphisms \mathbbTⁿ→\mathbbTⁿ with orientable expanding attractors of any topological dimension 1≤ q≤ n-1. We also prove that given any closed n-manifold Mⁿ, n≥ 2, and any d∈\1,…,[(n)/(2)]\, there is an axiom A diffeomorphism f: Mⁿ→ Mⁿ with a d-dimensional non-orientable expanding attractor. Similar statements hold for axiom A flows.

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