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Differentiability Properties of the Pressure of a Continuous Transformation on a Compact Metric Space
Author(s) -
Walters Peter
Publication year - 1992
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-46.3.471
Subject(s) - differentiable function , tangent space , mathematics , ergodic theory , pure mathematics , metric space , topological entropy , transformation (genetics) , function space , metric (unit) , continuous function (set theory) , space (punctuation) , uniform continuity , constant (computer programming) , tangent , topology (electrical circuits) , mathematical analysis , function (biology) , computer science , combinatorics , geometry , biochemistry , chemistry , operations management , evolutionary biology , biology , economics , gene , programming language , operating system
We study the topological pressure of a continuous transformation T with finite topological entropy on a compact metric space X . We give a family of examples which have a unique tangent functional at the constant function zero and the unique tangent functional is not ergodic. We obtain several necessary and sufficient conditions for the pressure of T to be Fréchet differentiable at a given f ɛ C ( X ).
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