Equicontinuity of iterates of circle maps release_iagpllgbfne6bcloodasnbsdd4

by Antonios Valaristos

Published in International Journal of Mathematics and Mathematical Sciences by Hindawi Limited.

1998   Volume 21, p453-458

Abstract

Let<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$f$"><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 xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="\[ \left\{ {f^n } \right\}_{n = 1}^\infty \] "><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>∞</mml:mi></mml:msubsup></mml:mrow></mml:math>to be equicontinuous.
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