•  
  •  
 

Acta of Turin Polytechnic University in Tashkent

Abstract

In this work we prove that the conjugacy between critical circle homeomorphisms with non integer criticality and linear rotation is singular function.

First Page

25

Last Page

27

References

  1. I. P. Cornfeld, S. V. Fomin, and Ya. G. Sinai, Ergodic theory, vol. 245, Springer, Berlin, Germany, 1982.
  2. M. Herman, “Sur la conjugaison diffe’rentiable des diffe’omorphismes du cercle a’ des rotations”, Institut des Hautes E’tudes Scientiiques, vol. 49, pp. 5–234, 1979.
  3. Y. Katznelson and D. Ornstein, “The differentiability of the conjugation of certain diffeomorphisms of the circle,” Ergodic theory and Dynamical Systems, vol. 9, no.4, pp.643–680, 1989.
  4. Y. Katznelson and D. Ornstein, “The absolute continuity of the conjugation of certain diffeomorphisms of the circle,” Ergodic theory and Dynamical Systems, vol. 9, no.4, pp.681–690, 1989.
  5. K. M. Khanin and Ya. G. Sinai, “Smoothness of conjugacies of diffeomorphisms of the circle with rotations,” Russian Mathematical Surveys, vol.44, no.1, pp.69–99, 1989, translation of Uspekhi Matematicheskikh Nauk,vol.44, pp.57–82, 1989.
  6. J.-C. Yoccoz, “Il n’y a pas de contre-exemple de Denjoy analytique,” Comptes Rendus des Se’ances de l’Acade’mie des Sciences, vol. 298, no. 7, pp. 141–144, 1984.
  7. G. Swiątek, “On critical circle homeomorphisms,” Boletim da Sociedade Brasileira de Matematica,vol.29, no.2,pp.329–351, 1998.
  8. J. Graczyk and G. Swiątek, “Singular measures in circle dynamics,” Communications

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.