Non-standard smooth realizations of Liouville rotations

DOI10.1017/S0143385707000314zbMath1127.37008arXivmath/0608322MaRDI QIDQ5436451

Bassam Fayad, Alistair Windsor, Maria Saprykina

Publication date: 16 January 2008

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0608322

zbMATH Keywords

unique ergodicityvolume-preserving diffeomorphismsrotations of the circlemeasure-theoretic isomorphismconjugation approximation method

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Ergodicity, mixing, rates of mixing (37A25) Dynamical systems involving maps of the circle (37E10) Rotation numbers and vectors (37E45)

Related Items (15)

Smooth diffeomorphisms with homogeneous spectrum and disjointness of convolutions ⋮ Weakly mixing diffeomorphisms preserving a measurable Riemannian metric with prescribed Liouville rotation behavior ⋮ Smooth zero-entropy diffeomorphisms with ergodic derivative extension ⋮ Slow entropy for some Anosov-Katok diffeomorphisms ⋮ An uncountable family of pairwise non-Kakutani equivalent smooth diffeomorphisms ⋮ Real-analytic realization of uniform circular systems and some applications ⋮ Non-standard real-analytic realizations of some rotations of the circle ⋮ Real-analytic weak mixing diffeomorphisms preserving a measurable Riemannian metric ⋮ Analytic uniquely ergodic volume preserving maps on odd spheres ⋮ A smooth zero-entropy diffeomorphism whose product with itself is loosely Bernoulli ⋮ A symbolic representation for Anosov-Katok systems ⋮ Dimensional characteristics of invariant measures for circle diffeomorphisms ⋮ Real-analytic AbC constructions on the torus ⋮ Spectral disjointness of powers of diffeomorphisms with arbitrary Liouvillean rotation behavior ⋮ Uniform rigidity sequences for weak mixing diffeomorphisms on \(\mathbb{D}^2\), \(\mathbb{A}\) and \(\mathbb{T}^2\)

Cites Work

• Analytic nonlinearizable uniquely ergodic diffeomorphisms on \mathbb T^{\mathbf{2}}
• Constructions in elliptic dynamics

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