Entropy and periodic points for transitive maps

Abstract

The aim of this paper is to investigate the connection between transitivity, density of the set of periodic points and topological entropy for low dimensional continuous maps. The paper deals with this problem in the case of the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding="application/x-tex">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>–star and the circle among the one–dimensional spaces and in some higher dimensional spaces. Particular attention is paid to triangular maps and to extensions of transitive maps to higher dimensions without increasing topological entropy.