Renormalization theory for multimodal maps

Abstract

We study the dynamics of the renormalization operator for multimodal maps. In particular, we prove the exponential convergence of this operator for infinitely renormalizable maps with same bounded combinatorial type.

37 pages, 4 figures

Cited by in corpus (8)

• Puzzle geometry and rigidity: The Fibonacci cycle is hyperbolic
• Quasisymmetric rigidity in one-dimensional dynamics
• Asymmetric unimodal maps with non-universal period-doubling scaling laws
• Dynamics of asymptotically holomorphic polynomial-like maps
• Shy shadows of infinite-dimensional partially hyperbolic invariant sets
• The boundary of chaos for interval mappings
• Renormalization of symmetric bimodal maps with low smoothness
• The full renormalization horseshoe for multimodal maps