ON DYNAMICS OF CIRCLE MAPS

Puneet Sharma (India) and Anima Nagar (India)

Received August 22, 2007; Revised October 23, 2007

Abstract

For self maps on the circle, we study relations between periodic points of the circle map and its lift. Further we give a quite simple number theoretic proof for circle maps of degree 2 or more to have periodic points of all periods. For such maps we study sensitivity, topological entropy, transitivity and especially show that here all forms of transitivity are equivalent. Also, we study some properties of commuting circle maps.

Keywords and phrases: circle maps, lift, periodic point, transitivity, sensitive, topological entropy, commuting maps.