Geodesic
Invariant sets with zero measure and full Hausdorff dimension
Barreira, Luis1 ; Schmeling, Jörg2
1 Departamento de Matemática, Instituto Superior Técnico, 1096 Lisboa, Portugal
2 Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 2-6, D–14195 Berlin, Germany
Electronic research announcements of the American Mathematical Society, Tome 03 (1997), pp. 114-118 Cet article a éte moissonné depuis la source American Mathematical Society

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For a subshift of finite type and a fixed Hölder continuous function, the zero measure invariant set of points where the Birkhoff averages do not exist is either empty or carries full Hausdorff dimension. Similar statements hold for conformal repellers and two-dimensional horseshoes, and the set of points where the pointwise dimensions, local entropies, Lyapunov exponents, and Birkhoff averages do not exist simultaneously.
DOI : 10.1090/S1079-6762-97-00035-8

Barreira, Luis 1 ; Schmeling, Jörg 2

1 Departamento de Matemática, Instituto Superior Técnico, 1096 Lisboa, Portugal
2 Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 2-6, D–14195 Berlin, Germany 
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Barreira, Luis; Schmeling, Jörg. Invariant sets with zero measure and full Hausdorff dimension. Electronic research announcements of the American Mathematical Society, Tome 03 (1997), pp. 114-118. doi: 10.1090/S1079-6762-97-00035-8

[1] Barreira, Luis, Pesin, Yakov, Schmeling, Jörg On the pointwise dimension of hyperbolic measures: a proof of the Eckmann-Ruelle conjecture Electron. Res. Announc. Amer. Math. Soc. 1996 69 72

[2] Pesin, Ya. B., Pitskel′, B. S. Topological pressure and the variational principle for noncompact sets Funktsional. Anal. i Prilozhen. 1984

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