TY - JOUR
T1 - SMOOTH RIGIDITY FOR CODIMENSION ONE ANOSOV FLOWS
AU - Gogolev, Andrey
AU - Hertz, Federico Rodriguez
N1 - Publisher Copyright:
© 2023 by the authors.
PY - 2023/7/1
Y1 - 2023/7/1
N2 - We introduce the matching functions technique in the setting of Anosov flows. Then we observe that simple periodic cycle functionals (also known as temporal distances) provide a source of matching functions for conjugate Anosov flows. For conservative codimension one Anosov flows ϕt : M Ñ M, dim M ě 4, these simple periodic cycle functionals are C1 regular and, hence, can be used to improve regularity of the conjugacy. Specifically, we prove that a continuous conjugacy must, in fact, be a C1 diffeomorphism for an open and dense set of codimension one conservative Anosov flows.
AB - We introduce the matching functions technique in the setting of Anosov flows. Then we observe that simple periodic cycle functionals (also known as temporal distances) provide a source of matching functions for conjugate Anosov flows. For conservative codimension one Anosov flows ϕt : M Ñ M, dim M ě 4, these simple periodic cycle functionals are C1 regular and, hence, can be used to improve regularity of the conjugacy. Specifically, we prove that a continuous conjugacy must, in fact, be a C1 diffeomorphism for an open and dense set of codimension one conservative Anosov flows.
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U2 - 10.1090/proc/16177
DO - 10.1090/proc/16177
M3 - Article
AN - SCOPUS:85174946610
SN - 0002-9939
VL - 151
SP - 2975
EP - 2988
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 7
ER -