Journal of the Korean Mathematical Society (J. Korean Math. Soc.) (20040101), 41, no.~6, 1087-1099. ISSN: 0304-9914 (print).eISSN: 2234-3008.
Subject
28 Measure and integration -- 28D Measure-theoretic ergodic theory 28D10 One-parameter continuous families of measure-preserving transformations 28D20 Entropy and other invariants
37 Dynamical systems and ergodic theory -- 37B Topological dynamics 37B40 Topological entropy
37 Dynamical systems and ergodic theory -- 37D Dynamical systems with hyperbolic behavior 37D35 Thermodynamic formalism, variational principles, equilibrium states
This paper is devoted to the study of the thermodynamic formalism for flows without fixed points. The authors adapt to this context the characterization of metric entropy introduced by A. Katok [Inst. Hautes Études Sci. Publ. Math. No. 51 (1980), 137--173; MR0573822 (81i:28022)] for ergodic measures, using spanning sets. This allows them to get a natural result on the variational principle relating topological pressure to metric pressures, stating that the supremum can be restricted to the measures which are ergodic for the flow. \par Finally, they prove that the properties that the topological pressure is zero, nonzero, finite or infinite are invariant under weak equivalence. This is a generalization of work in [T. Ohno, Publ. Res. Inst. Math. Sci. {\bf 16} (1980), no.~1, 289--298; MR0574037 (81g:54053)], where this result was established for the topological entropy.