Semigroup Actions of Expanding Maps.
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| Title: | Semigroup Actions of Expanding Maps. |
|---|---|
| Authors: | Carvalho, Maria1 mpcarval@fc.up.pt, Rodrigues, Fagner2 fagnerbernardini@gmail.com, Varandas, Paulo3 paulo.varandas@ufba.br |
| Source: | Journal of Statistical Physics. Jan2017, Vol. 166 Issue 1, p114-136. 23p. |
| Subjects: | Ruelle operators, Zeta functions, Thermodynamic equilibrium, Semigroup algebras, Topological entropy, Ergodic theory |
| Abstract: | We consider semigroups of Ruelle-expanding maps, parameterized by random walks on the free semigroup, with the aim of examining their complexity and exploring the relation between intrinsic properties of the semigroup action and the thermodynamic formalism of the associated skew-product. In particular, we clarify the connection between the topological entropy of the semigroup action and the growth rate of the periodic points, establish the main properties of the dynamical zeta function of the semigroup action and relate these notions to recent research on annealed and quenched thermodynamic formalism. Meanwhile, we examine how the choice of the random walk in the semigroup unsettles the ergodic properties of the action. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Statistical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: Semigroup Actions of Expanding Maps. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Carvalho%2C+Maria%22">Carvalho, Maria</searchLink><relatesTo>1</relatesTo><i> mpcarval@fc.up.pt</i><br /><searchLink fieldCode="AR" term="%22Rodrigues%2C+Fagner%22">Rodrigues, Fagner</searchLink><relatesTo>2</relatesTo><i> fagnerbernardini@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Varandas%2C+Paulo%22">Varandas, Paulo</searchLink><relatesTo>3</relatesTo><i> paulo.varandas@ufba.br</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Statistical+Physics%22">Journal of Statistical Physics</searchLink>. Jan2017, Vol. 166 Issue 1, p114-136. 23p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Ruelle+operators%22">Ruelle operators</searchLink><br /><searchLink fieldCode="DE" term="%22Zeta+functions%22">Zeta functions</searchLink><br /><searchLink fieldCode="DE" term="%22Thermodynamic+equilibrium%22">Thermodynamic equilibrium</searchLink><br /><searchLink fieldCode="DE" term="%22Semigroup+algebras%22">Semigroup algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Topological+entropy%22">Topological entropy</searchLink><br /><searchLink fieldCode="DE" term="%22Ergodic+theory%22">Ergodic theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We consider semigroups of Ruelle-expanding maps, parameterized by random walks on the free semigroup, with the aim of examining their complexity and exploring the relation between intrinsic properties of the semigroup action and the thermodynamic formalism of the associated skew-product. In particular, we clarify the connection between the topological entropy of the semigroup action and the growth rate of the periodic points, establish the main properties of the dynamical zeta function of the semigroup action and relate these notions to recent research on annealed and quenched thermodynamic formalism. Meanwhile, we examine how the choice of the random walk in the semigroup unsettles the ergodic properties of the action. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Statistical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10955-016-1697-3 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 23 StartPage: 114 Subjects: – SubjectFull: Ruelle operators Type: general – SubjectFull: Zeta functions Type: general – SubjectFull: Thermodynamic equilibrium Type: general – SubjectFull: Semigroup algebras Type: general – SubjectFull: Topological entropy Type: general – SubjectFull: Ergodic theory Type: general Titles: – TitleFull: Semigroup Actions of Expanding Maps. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Carvalho, Maria – PersonEntity: Name: NameFull: Rodrigues, Fagner – PersonEntity: Name: NameFull: Varandas, Paulo IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan2017 Type: published Y: 2017 Identifiers: – Type: issn-print Value: 00224715 Numbering: – Type: volume Value: 166 – Type: issue Value: 1 Titles: – TitleFull: Journal of Statistical Physics Type: main |
| ResultId | 1 |
