Differentiable circle maps with a flat interval

DOI10.1007/BF02101658zbMath0840.58038OpenAlexW2079677464MaRDI QIDQ1907965

F. M. Tangerman, Jacek Graczyk, J. J. P. Veerman, Leo B. Jonker, Grzegorz Świątek

Publication date: 6 March 1996

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

Full work available at URL: https://doi.org/10.1007/bf02101658

zbMATH Keywords

Hausdorff dimensionnon-wandering setLebesgue measureflat intervalweakly order preserving circle maps

Mathematics Subject Classification ID

Ergodic theory (37A99) Hausdorff and packing measures (28A78) Dynamical systems over complex numbers (37F99)

Related Items (14)

The flat spot standard family: variation of the entrance time median ⋮ A phase transition for circle maps and Cherry flows ⋮ Critical circle maps near bifurcation ⋮ Invariant measures for Cherry flows ⋮ Cherry flow: physical measures and perturbation theory ⋮ Cherry flows with non-trivial attractors ⋮ Unbounded regime for circle maps with a flat interval ⋮ A phase transition for circle maps with a flat spot and different critical exponents ⋮ Quasi-symmetric conjugacy for circle maps with a flat interval ⋮ The rigidity conjecture ⋮ Fractal Fourier spectra of Cherry flows ⋮ A Denjoy counterexample for circle maps with an half-critical point ⋮ Cherry Maps with Different Critical Exponents: Bifurcation of Geometry ⋮ Invariant manifolds for non-differentiable operators

Cites Work

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• Scalings in circle maps. I
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• Rational rotation numbers for maps of the circle
• Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps
• A structure theorem in one dimensional dynamics
• Critical circle maps near bifurcation
• On Cherry flows
• Global phase space universality, smooth conjugacies and renormalisation. I. The C^{1+ α}case
• On the structure of the family of Cherry fields on the torus
• One-dimensional dynamics: The Schwarzian derivative and beyond
• Irrational rotation numbers
• The Fibonacci Unimodal Map
• Rotation intervals for a class of maps of the real line into itself

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