There are no σ-finite absolutely continuous invariant measures for multicritical circle maps *

DOI10.1088/1361-6544/ac1a02zbMath1483.37050arXiv2007.10444OpenAlexW3194935856MaRDI QIDQ5010054

Pablo Guarino, Edson de Faria

Publication date: 24 August 2021

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.10444

zbMATH Keywords

critical circle maps\(\sigma\)-finite measuresKatznelson's criterion

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Periodic orbits of vector fields and flows (37C27) Universality and renormalization of dynamical systems (37E20)

Related Items (7)

Quasisymmetric orbit-flexibility of multicritical circle maps ⋮ Renormalization of analytic multicritical circle maps with bounded type rotation numbers ⋮ Renormalization of bicritical circle maps ⋮ Automorphic measures and invariant distributions for circle dynamics ⋮ Invariant measure of a circle map with a mixed type of singularities ⋮ Dynamics of multicritical circle maps ⋮ Note on Lyapunov exponent for critical circle maps

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• Rigidity of critical circle mappings. I
• A Denjoy counterexample for circle maps with an half-critical point
• A C^∞ Denjoy counterexample
• Universal estimates for critical circle mappings
• Real bounds and quasisymmetric rigidity of multicritical circle maps

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