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Non-standard real-analytic realizations of some rotations of the circle

Published online by Cambridge University Press:  28 December 2015

SHILPAK BANERJEE
SHILPAK BANERJEE*
Affiliation:
Department of Mathematics, Pennsylvania State University, McAllister Building, University Park, Pennsylvania, 16802, USA email banerjee.shilpak@gmail.com
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Abstract

We extend some aspects of the smooth approximation by conjugation method to the real-analytic set-up, and create examples of zero entropy, uniquely ergodic, real-analytic diffeomorphisms of the two-dimensional torus that are metrically isomorphic to some (Liouvillian) irrational rotations of the circle.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 5 , August 2017 , pp. 1369 - 1386
Copyright
© Cambridge University Press, 2015 

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References

Anosov, D. V. and Katok, A.. New examples in smooth ergodic theory. Trans. Moscow Math. Soc. 23 (1970), 1–35.Google Scholar
Benhenda, M.. Non-standard smooth realization of shifts on the torus. J. Mod. Dyn. 7(3) (2013), 329–367.Google Scholar
Benhenda, M.. A smooth Gaussian-Kronecker diffeomorphism. Preprint, https://hal.archives-ouvertes.fr/hal-00869084.Google Scholar
Fayad, B. R. and Katok, A.. Constructions in elliptic dynamics. Ergod. Th. & Dynam. Sys. 24(5) (2004), 1477–1520.Google Scholar
Fayad, B. R. and Katok, A.. Analytic uniquely ergodic volume preserving maps on odd spheres. Comment. Math. Helv. 89(4) (2014), 963–977.Google Scholar
Fayad, B. R., Saprykina, M. and Windsor, A.. Non-Standard smooth realizations of Liouville rotations. Ergod. Th. & Dynam. Sys. 27(6) (2007), 1803–1818.Google Scholar
Gunesch, R. and Katok, A.. Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure. Discrete Contin. Dyn. Syst. 6(1) (2000), 61–88.Google Scholar
Katok, A.. Ergodic perturbations of degenerate integrable Hamiltonian systems. Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973), 539–576 (in Russian).Google Scholar
Kunde, P.. Real-analytic weak mixing diffeomorphisms preserving a measurable Riemannian metric. Preprint. Ergod. Th. & Dynam. Sys. accepted.Google Scholar
Saprykina, M.. Analytic non-linearizable uniquely ergodic diffeomorphisms on 𝕋2 . Ergod. Th. & Dynam. Sys. 23(3) (2003), 935–955.Google Scholar