Following the scheme inspired by Tsallis [Jagannathan & Sudeshna, 2005; Patidar & Sud, 2009], we study the Gaussian map and its [Formula: see text]-deformed version. We compute the topological entropies of the discrete dynamical systems which are obtained for both maps, the original Gaussian map and its [Formula: see text]-modification. In particular, we are able to obtain the parametric region in which the topological entropy is positive. The analysis of the sign of Schwarzian derivative and the topological entropy allow us a deeper analysis of the dynamics. We also highlight the coexistence of attractors, even if it is possible to determine a wide range of parameters in which one of them is a chaotic attractor.

中文翻译：

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q-变形高斯映射的动力学

遵循受 Tsallis 启发的方案 [Jagannathan & Sudeshna, 2005; Patidar & Sud, 2009]，我们研究了高斯图及其 [公式：见文本] 变形版本。我们计算离散动力系统的拓扑熵，这些系统是从两个地图、原始高斯地图及其[公式：见文本]修改中获得的。特别是，我们能够获得拓扑熵为正的参数区域。对 Schwarzian 导数的符号和拓扑熵的分析使我们能够对动力学进行更深入的分析。我们还强调了吸引子的共存，即使可以确定其中一个是混沌吸引子的广泛参数。