Interval maps quasi-symmetrically conjugated to a piecewise affine map

2013/09/29 by Huaibin Li, Li, Huaibin
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS

paper · pdf · doi:10.48550/arxiv.1309.7593

arXiv admin note: text overlap with arXiv:1204.3071, arXiv:1005.2640 by other authors

arxiv created 2013/09/29 · arxiv updated 2013/10/01

Abstract

Consider a multimodal interval map f of C³ with non-flat critical points. We establish several characterizations of the map f is quasi-symmetrically conjugated to a piecewise affine map in the case f is topologically exact and all of its periodic points are hyperbolic repelling. In particular, we give a negative answer to a question posted by Henk Bruin in \citeBru96.

Citations

• Asymptotic expansion of smooth interval maps
• The maximal entropy measure detects non-uniform hyperbolicity

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