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Localized topological pressure and equilibrium states

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Tamara Kucherenko, Christian Wolf

Dynamical Systems · Submitted 15 Oct 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In particular, ergodic localized equilibrium states for H\"older continuous potentials are in general not unique.

how it is stated · asserted 0.98 read the record →

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arXiv ID1310.4030 (version 1)
Pith IDWOFX26VI, Pith's permanent record of this paper and its review
CitationChristian Wolf, Tamara Kucherenko. "Localized topological pressure and equilibrium states." arXiv:1310.4030 (2013). https://pith.science/paper/WOFX26VI
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,952 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.68 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.74 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We introduce the notion of localized topological pressure for continuous maps on compact metric spaces. The localized pressure of a continuous potential $\varphi$ is computed by considering only those $(n,\epsilon)$-separated sets whose statistical sums with respect to an $m$-dimensional potential $\Phi$ are "close" to a given value $w\in \bR^m$. We then establish for several classes of systems and potentials $\varphi$ and $\Phi$ a local version of the variational principle. We also construct examples showing that the assumptions in the localized variational principle are fairly sharp. Next, we study localized equilibrium states and show that even in the case of subshifts of finite type and H\"older continuous potentials, there are several new phenomena that do not occur in the theory of classical equilibrium states. In particular, ergodic localized equilibrium states for H\"older continuous potentials are in general not unique.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We introduce the notion of localized topological pressure for continuous maps on compact metric spaces. contribution 1.00 0.95 0.06 asserted 0.99
s1 The localized pressure of a continuous potential $\varphi$ is computed by considering only those $(n,\epsilon)$-separated sets whose statistical sums with respect to an $m$-dimensional potential $\Phi$ are "close" to a given value $w\in \bR^m$. method 0.67 0.73 0.07 asserted 1.00
s2 We then establish for several classes of systems and potentials $\varphi$ and $\Phi$ a local version of the variational principle. result 0.65 0.96 0.22 asserted 1.00
s3 We also construct examples showing that the assumptions in the localized variational principle are fairly sharp. result 0.48 0.96 0.07 asserted 1.00
s4 Next, we study localized equilibrium states and show that even in the case of subshifts of finite type and H\"older continuous potentials, there are several new phenomena that do not occur in the theory of classical equilibrium states. contribution 0.85 0.95 0.24 asserted 1.00
s5 In particular, ergodic localized equilibrium states for H\"older continuous potentials are in general not unique. result 0.99 0.91 0.31 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from proof or derivation 1.00.

What was examined, and what was not

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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We introduce the notion of localized topological pressure for continuous maps on compact metric spaces. The localized pressure of a continuous potential $\varphi$ is computed by considering only those $(n,\epsilon)$-separated sets whose statistical sums with respect to an $m$-dimensional potential $\Phi$ are "close" to a given value $w\in \bR^m$. We then establish for several classes of systems and potentials $\varphi$ and $\Phi$ a local version of the variational principle. We also construct examples showing that the assumptions in the localized variational principle are fairly sharp. Next, we study localized equilibrium states and show that even in the case of subshifts of finite type and H\"older continuous potentials, there are several new phenomena that do not occur in the theory of classical equilibrium states. In particular, ergodic localized equilibrium states for H\"older continuous potentials are in general not unique.

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1 arXiv paper cite this in 3 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 2 sentences without a confident label

Compares with it 1 paper
  • The second result states existence and uniqueness of equilibrium states under linear constraints; it is very close to Theorem B of [ref] , but even disregarding the difference in our hypotheses we obtain a more precise description of the equilibrium state: the parameter $s$ of [ref] is always equal to $1$.

    The calculus of thermodynamical formalism · Applications to equilibrium states · 0.98

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