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We study behavior of the topological entropy as the function of parameters for two-parameter family of symmetric Lorenz maps Tc,ɛ(x) = (−1 + c|x|1−ɛ) · sgn(x). This is the normal form for splitting the homoclinic loop in systems which have a saddle equilibrium with one-dimensional unstable manifold and zero saddle value. Due to L.P. Shilnikov resul...
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... topological entropy as the function of the parameter c. Note that the problems of monotonicity of topological entropy was considered for specific families of one dimensional maps by several authors. In [9], [10] it has been proven that for quadratic maps x 2 + c, the topological entropy is a monotone (non strictly) increasing function of c (see fig. 3 for the logistic family, which is actually the same after change of coordinates). In recent paper [11], the monotonicity result was proven for the family x + c with large (not necessarily integer). Our family of maps is different from those families in the sense that we allow infinite derivatives at the discontinuity point, which makes ...
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