On the hyperbolicity of Lorenz renormalization

DOI10.1007/s00220-013-1858-zzbMath1296.37031arXiv1205.0829OpenAlexW3105924769MaRDI QIDQ393704

Marco Martens, Björn Winckler

Publication date: 24 January 2014

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.0829

zbMATH Keywords

Hausdorff dimensionattractorcombinatorial dynamicsinfinitely renormalizableLorenz mapuniquely ergodic

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Dynamical systems with hyperbolic orbits and sets (37D05) Dynamical systems involving maps of the interval (37E05) Combinatorial dynamics (types of periodic orbits) (37E15) Universality and renormalization of dynamical systems (37E20) Computational methods for bifurcation problems in dynamical systems (37M20)

Related Items

The symplectic structure for renormalization of circle diffeomorphisms with breaks ⋮ The Lorenz Renormalization Conjecture ⋮ Renormalization for Lorenz maps of monotone combinatorial types ⋮ Rigidity for piecewise smooth circle homeomorphisms and certain GIETs ⋮ A priori bounds for GIETs, affine shadows and rigidity of foliations in genus two ⋮ Asymmetric unimodal maps with non-universal period-doubling scaling laws ⋮ A phase transition for circle maps with a flat spot and different critical exponents ⋮ Existence of \(C^k\)-invariant foliations for Lorenz-type maps ⋮ Physical measures for infinitely renormalizable Lorenz maps ⋮ The rigidity conjecture ⋮ Nonexistence of wandering domains for strongly dissipative infinitely renormalizable Hénon maps at the boundary of chaos ⋮ Renormalization of symmetric bimodal maps with low smoothness ⋮ Hyperbolicity of renormalization for dissipative gap mappings

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