Renormalization of H\'enon map in arbitrary dimension I : Universality and reduction of ambient space
Abstract
Period doubling H\'enon 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 Cr 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 H\'enon-like map in arbitrary finite dimension.
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