On a question of Katok in one-dimensional case

Pages: 1209 - 1213, Volume 24, Issue 4, August 2009

doi:10.3934/dcds.2009.24.1209       Abstract        Full Text (103.7K)

Yunping Jiang - Department of Mathematics, Queens College of CUNY, Flushing, NY 11367, United States (email)

Abstract: We prove that a $C^{1}$ orientation-preserving circle endomorphism which is Hölder conjugate to a $C^{1}$ circle expanding endomorphism is itself expanding.

Keywords:  expanding endomorphism, Hölder conjugacy.
Mathematics Subject Classification:  Primary: 37D2015; Secondary: 37E10.

Received: August 2008;      Revised: November 2008;      Published: May 2009.