Let <mml:math alttext="$f$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi></mml:math> be a continuous map of the circle to itself. Necessary and sufficient conditions are given for the family ofiterates <mml:math alttext="\[ \left\{ {f^n } \right\}_{n = 1}^\infty   \] " xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msup><mml:mi>f</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>&#8734;</mml:mi></mml:msubsup></mml:mrow></mml:math>
 to be equicontinuous.

International Journal of Mathematics and Mathematical Sciences

Equicontinuity of iterates of circle maps

Abstract

Copyright