Pianigiani-Yorke measures for non-Hölder continuous potentials (Q1392515)

This paper is devoted to the Pianigiani-Yorke measures for non-Hölder continuous potentials. The author proves that each non-Hölder continuous potential has a Pianigiani-Yorke measure for a Markovian factor of a topologically mixing Markov chain under a weak condition. The proof is based on the well-known thermodynamic formalism. The author gives a uniqueness condition of the Pianigiani-Yorke measure together with a concrete example which shows that the condition is essential.