Self-similar constructions in smooth dynamics: Rigidity, smoothness and dimension

DOI10.1007/BF02096564zbMath0771.58035OpenAlexW2049512046MaRDI QIDQ1208341

Charles Tresser, Jean-Marc Gambaudo

Publication date: 16 May 1993

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

Full work available at URL: https://doi.org/10.1007/bf02096564

zbMATH Keywords

dynamical systemsself-similarityperiod-doubling bifurcationuniversality in physicssmooth dynamics

Mathematics Subject Classification ID

Smooth approximations in differential topology (57R12) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (5)

Liapunov stability and adding machines ⋮ Nielsen-Thurston reducibility and renormalization ⋮ Infinitely renormalizable diffeomorphisms of the disk at the boundary of chaos ⋮ Fractals as objects with nontrivial structures at all scales ⋮ The real analytic Feigenbaum–Coullet–Tresser attractor in the disc

Cites Work

• Period doubling bifurcations for families of maps on \(R^ n\)
• \(C^ 2\) counterexamples to the Seifert conjecture
• Counterexamples to the Seifert conjecture and opening closed leaves of foliations
• The periodic points of maps of the disk and the interval
• Quantitative universality for a class of nonlinear transformations
• On the nature of turbulence
• Diffeomorphisms with infinitely many strange attractors
• Henon-like maps with strange attractors: there exist C^∞Kupka-Smale diffeomorphisms on S²with neither sinks nor sources
• Bifurcation of an attracting invariant circle: a Denjoy attractor
• Strange Attractors of Uniform Flows

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