Dynamics of deformed Henon-like map

A B S T R A C T In this paper, we introduce q-deformation on Henon-like maps and discuss various dynamical properties of newly deformed system, named as q-Henon map. We describe a method for the construction of superstable periodic cycles and their accumulation on the parameter space for different deformed parameters. At the accumulation, the q-Henon map undergoes transition from periodic to chaotic behaviour. For restricted range of q , we achieve chaos prior to the canonical Henon-like maps. This leads to the paradoxical behaviour. Further, we use the concept of heteroclinic web to discuss the heteroclinic bifurcation and the Cantor attractor of infinitely renormalizable q-Henon maps. Finally, we show that the basin of attraction of q-Henon maps do not have an escaping region for a particular set of deformed parameters.(c) 2021 Elsevier Ltd. All rights reserved.