Semi-conjugacies between m-horseshoe maps and n-horseshoe maps
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.