Please use this identifier to cite or link to this item: https://hdl.handle.net/11000/30984

Entropy Monotonicity and Superstable Cycles for the Quadratic Family Revisited

Title:
Entropy Monotonicity and Superstable Cycles for the Quadratic Family Revisited
Authors:
Giménez, Ángel
AMIGO, JOSE M.  
Editor:
MDPI
Department:
Departamentos de la UMH::Estadística, Matemáticas e Informática
Issue Date:
2020
URI:
https://hdl.handle.net/11000/30984
Abstract:
The main result of this paper is a proof using real analysis of the monotonicity of the topological entropy for the family of quadratic maps, sometimes called Milnor’s Monotonicity Conjecture. In contrast, the existing proofs rely in one way or another on complex analysis. Our proof is based on tools and algorithms previously developed by the authors and collaborators to compute the topological entropy of multimodal maps. Specifically, we use the number of transverse intersections of the map iterations with the so-called critical line. The approach is technically simple and geometrical. The same approach is also used to briefly revisit the superstable cycles of the quadratic maps, since both topics are closely related.
Keywords/Subjects:
topological entropy
quadratic maps
Milnor’s Monotonicity Conjecture
superstable cycles
root branches
transversality
Knowledge area:
CDU: Ciencias puras y naturales
Type of document:
application/pdf
Access rights:
info:eu-repo/semantics/openAccess
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
DOI:
https://doi.org/10.3390/e22101136
Appears in Collections:
Artículos Estadística, Matemáticas e Informática



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