On specification and measure expansiveness
Welington Cordeiro Manfred Denker Xuan Zhang

We relate the local specification and periodic shadowing properties. We also clarify the relation between local weak specification and local specification if the system is measure expansive. The notion of strong measure expansiveness is introduced, and an example of a non-expansive systems with the strong measure expansive property is given. Moreover, we find a family of examples with the $N$-expansive property, which are not strong measure expansive. We finally show a spectral decomposition theorem for strong measure expansive dynamical systems with shadowing.

keywords: Specification expansiveness shadowing topologically mixing spectral theorem
Thermodynamic formalism for random countable Markov shifts
Manfred Denker Yuri Kifer Manuel Stadlbauer
We introduce a relative Gurevich pressure for random countable topologically mixing Markov shifts. It is shown that the relative variational principle holds for this notion of pressure. We also prove a relative Ruelle-Perron-Frobenius theorem which enables us to construct a wealth of invariant Gibbs measures for locally fiber Hölder continuous functions. This is accomplished via a new construction of an equivariant family of fiber measures using Crauel's relative Prohorov theorem. Some properties of the Gibbs measures are discussed as well.
keywords: variational principle random countable shifts thermodynamic formalism random transformations.
Corrigendum to: Thermodynamic formalism for random countable Markov shifts
Manfred Denker Yuri Kifer Manuel Stadlbauer
We correct a flaw in the proof of Proposition 6.3 in [1].
keywords: Random countable shifts random transformations. thermodynamic formalism variational principle
A note on specification for iterated function systems
Welington Cordeiro Manfred Denker Michiko Yuri
We introduce several notions of specification for iterated function systems and exhibit some of their dynamical properties. In particular, we show that topological entropy and algebraic pressure [4] of systems with specification are approximable by the corresponding expressions for finitely generated iterated function systems.
keywords: Iterated function system specification entropy pressure mixing.

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