Entropy, Pressure, Ground States and Calibrated Sub-actions for Linear Dynamics

Lopes, Artur O.; Vargas, Victor

doi:10.1007/s00574-022-00296-7

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

Publication Types

Select...

Article1

Relationship

Self Cite1

Independent0

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Also, in [27], the existence of weak accumulation points at zero temperature was proved for a wider class of positive recurrent potentials defined on topologically transitive countable Markov shifts satisfying suitable conditions. However, in [19], conditions were presented to guarantee the existence of ground states in a wider class of linear dynamical systems defined on Banach spaces of infinite dimension.…”

Section: Introductionmentioning

confidence: 99%

Existence of the zero-temperature limit of equilibrium states on topologically transitive countable Markov shifts

Beltrán

Curinao²,

Maldonado³

et al. 2022

Ergod. Th. Dynam. Sys.

Self Cite

View full text Add to dashboard Cite

Consider a topologically transitive countable Markov shift $\Sigma $ and a summable locally constant potential $\phi $ with finite Gurevich pressure and $\mathrm {Var}_1(\phi ) < \infty $ . We prove the existence of the limit $\lim _{t \to \infty } \mu _t$ in the weak $^\star $ topology, where $\mu _t$ is the unique equilibrium state associated to the potential $t\phi $ . In addition, we present examples where the limit at zero temperature exists for potentials satisfying more general conditions.

show abstract

Section: Introductionmentioning

confidence: 99%