Por favor, use este identificador para citar o enlazar este ítem: https://hdl.handle.net/11000/30984

Entropy Monotonicity and Superstable Cycles for the Quadratic Family Revisited

Título :
Entropy Monotonicity and Superstable Cycles for the Quadratic Family Revisited
Autor :
Giménez, Ángel
AMIGO, JOSE M.  
Editor :
MDPI
Departamento:
Departamentos de la UMH::Estadística, Matemáticas e Informática
Fecha de publicación:
2020
URI :
https://hdl.handle.net/11000/30984
Resumen :
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.
Palabras clave/Materias:
topological entropy
quadratic maps
Milnor’s Monotonicity Conjecture
superstable cycles
root branches
transversality
Área de conocimiento :
CDU: Ciencias puras y naturales
Tipo documento :
application/pdf
Derechos de acceso:
info:eu-repo/semantics/openAccess
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
DOI :
https://doi.org/10.3390/e22101136
Aparece en las colecciones:
Artículos Estadística, Matemáticas e Informática



Creative Commons La licencia se describe como: Atribución-NonComercial-NoDerivada 4.0 Internacional.