Ergodic properties of bimodal circle maps
Sign Up to like & getrecommendations! Published in 2017 at "Ergodic Theory and Dynamical Systems"
DOI: 10.1017/etds.2017.80
Abstract: We give conditions that characterize the existence of an absolutely continuous invariant probability measure for a degree one $C^{2}$ endomorphism of the circle which is bimodal, such that all its periodic orbits are repelling, and… read more here.
Keywords: bimodal circle; circle maps; ergodic properties; properties bimodal ... See more keywords
Suppression of quasiperiodicity in circle maps with quenched disorder.
Sign Up to like & getrecommendations! Published in 2022 at "Physical review. E"
DOI: 10.1103/physreve.106.l012202
Abstract: We show that introducing quenched disorder into a circle map leads to the suppression of quasiperiodic behavior in the limit of large system sizes. Specifically, for most parameters the fraction of disorder realizations showing quasiperiodicity… read more here.
Keywords: circle; quenched disorder; circle maps; quasiperiodicity ... See more keywords
Rigidity of critical circle maps
Sign Up to like & getrecommendations! Published in 2018 at "Duke Mathematical Journal"
DOI: 10.1215/00127094-2018-0017
Abstract: We prove that any two $C^4$ critical circle maps with the same irrational rotation number and the same odd criticality are conjugate to each other by a $C^1$ circle diffeomorphism. The conjugacy is $C^{1+\alpha}$ for… read more here.
Keywords: critical circle; circle maps; circle; rigidity critical ... See more keywords