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Semi-conjugacies between m-horseshoe maps and n-horseshoe maps
Semi-conjugacies between m-horseshoe maps and n-horseshoe maps
教师介绍

本讲教师:石勇国
所属学科:理科
人  气:395

课程介绍
摘要:The conjugacy problem is one of the central questions in dynamical systems. Many works have devoted to conjugacy problems of horseshoe maps with the same number of laps, which is a kind of continuous, piecewise monotone interval maps. This paper considers semi-conjugacies from m-horseshoe maps to n-horseshoe maps for m > n ≥ 2. We first give neworientation-preserving/reversing partition on their domains. Then by Matkowski's fixed point principle we prove the existence of semi-conjugacies from m-horseshoe maps to n-horseshoe maps. We construct some sequences of functions to approximate these semi-conjugacies, and show that these semi-conjugacies are Holder continuous and nowhere differentiable. Finally, an example is given for a piecewise linear 4-horseshoe maps and a piecewise linear 3-horseshoe map.

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