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| It is well-known that topological entropy. depends monotonically on the parameter in the family of quadratic maps. The same was proved by Milnor and Tresser for cubic maps, and recently monotonicity of entropy for polynomials of arbitrary degree was established
by Bruin and Van Strien. This means that the isentropes (i.e., level sets of entropy) are connected subset of parameter, but I will demonstrate in this talk that the topological shape of such sets can be very complicated still, and many questions remain open. |
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