Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-29T02:49:49.387Z Has data issue: false hasContentIssue false
  • English
  • Français

Diffeomorphisms which cannot be topologically conjugate to diffeomorphisms of a higher smoothness

Published online by Cambridge University Press:  11 February 2010

DMITRY TURAEV
DMITRY TURAEV*
Affiliation:
Imperial College, London SW7 2AZ, UK (email: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We provide examples of two-dimensional diffeomorphisms which cannot be topologically conjugate to any diffeomorphism of a higher smoothness.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 2 , April 2011 , pp. 563 - 569
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Belitskii, G.. Smooth classification of one-dimensional diffeomorphisms with hyperbolic fixed points. Sib. Math. J. 27 (1986), 801–804.CrossRefGoogle Scholar
[2]Downarowicz, T. and Newhouse, S.. Symbolic extensions and smooth dynamical systems. Invent. Math. 160 (2005), 453–499.CrossRefGoogle Scholar
[3]Filipkiewicz, R.. Isomorphisms between diffeomorphism groups. Ergod. Th. & Dynam. Sys. 2 (1982), 159–171.CrossRefGoogle Scholar
[4]Freedman, M. H. and He, Z.-X.. A remark on inherent differentiability. Proc. Amer. Math. Soc. 104 (1988), 1305–1310.CrossRefGoogle Scholar
[5]Harrison, J.. Unsmoothable diffeomorphisms. Ann. of Math. (2) 102 (1975), 85–94.CrossRefGoogle Scholar
[6]Harrison, J.. Unsmoothable diffeomorphisms on higher dimensional manifolds. Proc. Amer. Math. Soc. 73 (1979), 249–255.CrossRefGoogle Scholar
[7]Gonchenko, S., Turaev, D. and Shilnikov, L.. On models with structurally unstable Poincaré homoclinic curve. Soviet Math. Docl. 44 (1992), 422–425.Google Scholar
[8]Gonchenko, S., Turaev, D. and Shilnikov, L.. On Newhouse regions of two-dimensional diffeomorphisms close to a diffeomorphism with a nontransversal heteroclinic cycle. Proc. Steklov Inst. Math. 216 (1997), 70–118.Google Scholar
[9]Gonchenko, S., Turaev, D. and Shilnikov, L.. Homoclinic tangencies of any order in Newhouse regions. J. Math. Sci. 105 (2001), 1738–1778.CrossRefGoogle Scholar
[10]Gonchenko, S., Shilnikov, L. and Turaev, D.. Homoclinic tangencies of arbitrarily high orders in conservative and dissipative two-dimensional maps. Nonlinearity 20 (2007), 241–275.CrossRefGoogle Scholar
[11]Katok, A.. Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Publ. Math. Inst. Hautes Études Sci. 51 (1980), 137–173.CrossRefGoogle Scholar
[12]de Melo, W.. Moduli of stability of two-dimensional diffeomorphisms. Topology 19 (1980), 9–21.CrossRefGoogle Scholar
[13]Newhouse, S.. The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms. Publ. Math. Inst. Hautes Études Sci. 50 (1979), 101–151.CrossRefGoogle Scholar
[14]Palis, J.. A differentiable invariant of topological conjugacies and moduli of stability. Astérisque 51 (1978), 335–346.Google Scholar
[15]de Melo, W., Palis, J. and van Strien, S.. Characterising diffeomorphisms with modulus of stability one. Dynamical Systems and Turbulence, Warwick 1980 (Lectures Notes in Mathematics, 898). Eds. Rand, D. A. and Young, L.-S.. Springer, Berlin, 1981, pp. 266–285.CrossRefGoogle Scholar
[16]Rubin, M.. On the reconstruction of topological spaces from their groups of homeomorphisms. Trans. Amer. Math. Soc. 312 (1989), 487–538.CrossRefGoogle Scholar