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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.

Copyright 1997 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 03 (1997), pp. 114-118
• Publisher Identifier: S 1079-6762(97)00035-8
• 1991 Mathematics Subject Classification. Primary 58F15, 58F11
• Received by the editors September 2, 1997
• Posted on October 29, 1997
• Communicated by Svetlana Katok
• Comments (When Available)

Luis Barreira

Departamento de Matemática, Instituto Superior Técnico, 1096 Lisboa, Portugal

E-mail address: barreira@math.ist.utl.pt

URL: http://www.math.ist.utl.pt/~barreira/

Jörg Schmeling

Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 2-6, D-14195 Berlin, Germany

E-mail address: shmeling@math.fu-berlin.de

Luis Barreira was partially supported by the projects PRAXIS XXI, 2/2.1/MAT/199/94 and JNICT, PBIC/C/MAT/2140/95. Jörg Schmeling was supported by the Leopoldina-Forderpreis.