Stochastically stable chaos for q-deformed unimodal maps

In this paper, we describe the deformation schemes inspired by Heine and Tsallis in reference of q-deformed physical systems related to the quantum group structures and the statistical mechanics. We discuss the dynamics of deformed unimodal maps in particular q-logistic map and q-Gaussian map. We show that there exists a set of parameter values with positive measures, for which these deformed maps exhibits stochastically stable chaos. The deformed maps have chaotic behavior for a large space of deformed parameter q than the canonical maps. � 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.