Sensitive Dependence on Initial Conditions for an Example of Markov Map: Skewed Doubling Map

Abstract

Markov map is one example of interval maps where it is a piecewise ex-panding map and obeys the Markov property. One well-known example of Markov map is the doubling map, a map which has two subintervals with equal partitions. In this paper, we are interested to investigate another type of Markov map, the so-called skewed doubling map. This map is a more generalized map than the doubling map. Thus, the aims of this paper are to nd the xed points as well as the periodic points for the skewed doubling map and to investigate the sensitive dependence on initial conditions of this map. The method considered here is the cobweb diagram. Numerical results suggest that there exist dense of periodic orbits for this map. The sensitivity of this map to initial conditions is also veried where small differences in initial conditions give dierent behaviour of the orbits in the map.