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 · #Mathematical Dynamics and Fractals #Chaos control and synchronization #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1506.02223

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.

Related

• Hénon renormalization in arbitrary dimension : Invariant space under renormalization operator
• Renormalization of three dimensional Hénon map I : Reduction of ambient space
• Renormalization of C^r Hénon map : Two dimensional embedded map in three dimension
• Renormalization in the Henon family, I: universality but non-rigidity
• Invariant space under Hénon renormalization : Intrinsic geometry of Cantor attractor