TY - JOUR
T1 - Measures maximizing the entropy for kan endomorphisms
AU - N'uñez-Madariaga, Bárbara
AU - Ramírez, Sebastián A.
AU - Vásquez, Carlos H.
N1 - Publisher Copyright:
© 2021 Institute of Physics Publishing. All rights reserved.
PY - 2021
Y1 - 2021
N2 - In 1994, Kan provided the first example of maps with intermingled basins. The Kan example corresponds to a partially hyperbolic endomorphism defined on a surface, with the boundary exhibiting two intermingled hyperbolic physical measures. Both measures are supported on the boundary, and they also maximize the topological entropy. In this work, we prove the existence of a third hyperbolic measure supported in the interior of the cylinder that maximizes the entropy.We also prove this statement for a larger class of invariant measures of large class maps including perturbations of the Kan example.
AB - In 1994, Kan provided the first example of maps with intermingled basins. The Kan example corresponds to a partially hyperbolic endomorphism defined on a surface, with the boundary exhibiting two intermingled hyperbolic physical measures. Both measures are supported on the boundary, and they also maximize the topological entropy. In this work, we prove the existence of a third hyperbolic measure supported in the interior of the cylinder that maximizes the entropy.We also prove this statement for a larger class of invariant measures of large class maps including perturbations of the Kan example.
KW - Lyapunov exponents
KW - Measures maximizing the entropy
KW - Partial hyperbolicity
UR - http://www.scopus.com/inward/record.url?scp=85118137514&partnerID=8YFLogxK
U2 - 10.1088/1361-6544/ac1f79
DO - 10.1088/1361-6544/ac1f79
M3 - Article
AN - SCOPUS:85118137514
VL - 34
SP - 7255
EP - 7302
JO - Nonlinearity
JF - Nonlinearity
SN - 0951-7715
IS - 10
ER -