Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows

Anatole Katok; Gerhard Knieper; Howard Weiss

doi:10.1007/BF02099667

Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows

Anatole Katok, Gerhard Knieper, Howard Weiss

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

Abstract

This paper represents part of a program to understand the behavior of topological entropy for Anosov and geodesic flows. In this paper, we have two goals. First we obtain some regularity results for C¹ perturbations. Second, and more importantly, we obtain explicit formulas for the derivative of topological entropy. These formulas allow us to characterize the critical points of topological entropy on the space of negatively curved metrics.

Original language	English (US)
Pages (from-to)	19-31
Number of pages	13
Journal	Communications In Mathematical Physics
Volume	138
Issue number	1
DOIs	https://doi.org/10.1007/BF02099667
State	Published - May 1991

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/BF02099667

Cite this

@article{86c606bbeaca4193be442073a8df1489,

title = "Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows",

abstract = "This paper represents part of a program to understand the behavior of topological entropy for Anosov and geodesic flows. In this paper, we have two goals. First we obtain some regularity results for C1 perturbations. Second, and more importantly, we obtain explicit formulas for the derivative of topological entropy. These formulas allow us to characterize the critical points of topological entropy on the space of negatively curved metrics.",

author = "Anatole Katok and Gerhard Knieper and Howard Weiss",

year = "1991",

month = may,

doi = "10.1007/BF02099667",

language = "English (US)",

volume = "138",

pages = "19--31",

journal = "Communications In Mathematical Physics",

issn = "0010-3616",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows

AU - Katok, Anatole

AU - Knieper, Gerhard

AU - Weiss, Howard

PY - 1991/5

Y1 - 1991/5

N2 - This paper represents part of a program to understand the behavior of topological entropy for Anosov and geodesic flows. In this paper, we have two goals. First we obtain some regularity results for C1 perturbations. Second, and more importantly, we obtain explicit formulas for the derivative of topological entropy. These formulas allow us to characterize the critical points of topological entropy on the space of negatively curved metrics.

AB - This paper represents part of a program to understand the behavior of topological entropy for Anosov and geodesic flows. In this paper, we have two goals. First we obtain some regularity results for C1 perturbations. Second, and more importantly, we obtain explicit formulas for the derivative of topological entropy. These formulas allow us to characterize the critical points of topological entropy on the space of negatively curved metrics.

UR - http://www.scopus.com/inward/record.url?scp=0001812718&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001812718&partnerID=8YFLogxK

U2 - 10.1007/BF02099667

DO - 10.1007/BF02099667

M3 - Article

AN - SCOPUS:0001812718

SN - 0010-3616

VL - 138

SP - 19

EP - 31

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 1

ER -

Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this