Renormalization of Hénon map in arbitrary dimension I : Universality and reduction of ambient space

2015/06/07 by Young Woo Nam, Nam, Young Woo
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:37F25

paper · pdf · doi:10.48550/arxiv.1506.02223

42 pages, 2 figures. arXiv admin note: text overlap with arXiv:1408.4289

arxiv created 2015/06/23 · arxiv updated 2015/06/24

Abstract

Period doubling Hénon renormalization of strongly dissipative maps is generalized in arbitrary finite dimension. In particular, a small perturbation of toy model maps with dominated splitting has invariant C^r surfaces embedded in higher dimension and the Cantor attractor has unbounded geometry with respect to full Lebesgue measure on the parameter space. It is an extension of dynamical properties of three dimensional infinitely renormalizable Hénon-like map in arbitrary finite dimension.

Citations

• Renormalization of three dimensional Hénon map I : Reduction of ambient space

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• Renormalization of three dimensional Hénon map I : Reduction of ambient space
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• Invariant space under Hénon renormalization : Intrinsic geometry of Cantor attractor