Period doubling for \(C^{2+\epsilon}\) mappings

DOI10.1007/BF02099549zbMath0906.58012OpenAlexW1570667378MaRDI QIDQ1918062

Alexander M. Davie

Publication date: 11 August 1996

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

Full work available at URL: https://doi.org/10.1007/bf02099549

zbMATH Keywords

spectrumstable manifoldperiod-doublingHölder functionGâteaux derivativerenormalization problems

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20) Iteration of real functions in one variable (26A18) Low-dimensional dynamical systems (37E99)

Related Items (7)

Homoclinic tangencies near cascades of period doubling bifurcations ⋮ The real analytic Feigenbaum–Coullet–Tresser attractor in the disc ⋮ Renormalization of symmetric bimodal maps with low smoothness ⋮ Hénon-like maps with arbitrary stationary combinatorics ⋮ Period tripling and quintupling renormalizations below \(C^2\) space ⋮ Dynamics of multicritical circle maps ⋮ Invariant manifolds for non-differentiable operators

Cites Work

• Unnamed Item
• The universal metric properties of nonlinear transformations
• Expanding direction of the period doubling operator
• Quantitative universality for a class of nonlinear transformations
• A computer-assisted proof of the Feigenbaum conjectures

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