TY - JOUR
T1 - Diffeomorphisms with infinitely many Smale horseshoes
AU - Zhang, Xu
AU - Chen, Guanrong
PY - 2024/12
Y1 - 2024/12
N2 - A class of planar diffeomorphims is formulated, with infinitely many coexisting Smale horseshoes, where the Lebesgue measure of the parameters with such strange dynamics is infinite. On each horseshoe, there exists a uniformly hyperbolic invariant set, on which the map is topologically conjugate to the two-sided full-shift on two symbols. Moreover, the topological entropy is infinite in certain parameter regions. © 2024 Informa UK Limited, trading as Taylor & Francis Group.
AB - A class of planar diffeomorphims is formulated, with infinitely many coexisting Smale horseshoes, where the Lebesgue measure of the parameters with such strange dynamics is infinite. On each horseshoe, there exists a uniformly hyperbolic invariant set, on which the map is topologically conjugate to the two-sided full-shift on two symbols. Moreover, the topological entropy is infinite in certain parameter regions. © 2024 Informa UK Limited, trading as Taylor & Francis Group.
KW - coexistence
KW - hyperbolic invariant set
KW - Smale horseshoe
KW - symbolic dynamical system
UR - http://www.scopus.com/inward/record.url?scp=85195945374&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85195945374&origin=recordpage
U2 - 10.1080/10236198.2024.2368170
DO - 10.1080/10236198.2024.2368170
M3 - RGC 21 - Publication in refereed journal
SN - 1023-6198
VL - 30
SP - 1866
EP - 1884
JO - Journal of Difference Equations and Applications
JF - Journal of Difference Equations and Applications
IS - 12
ER -