{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T12:10:14Z","timestamp":1760789414943,"version":"build-2065373602"},"reference-count":49,"publisher":"IOP Publishing","issue":"6","license":[{"start":{"date-parts":[[2022,5,26]],"date-time":"2022-05-26T00:00:00Z","timestamp":1653523200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2022,5,26]],"date-time":"2022-05-26T00:00:00Z","timestamp":1653523200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["CEECIND\/03721\/2017"],"award-info":[{"award-number":["CEECIND\/03721\/2017"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Nonlinearity"],"published-print":{"date-parts":[[2022,6,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We extend Margulis\u2013Ruelle inequality to the general setting of semigroup actions which are finitely generated either by Lipschitz continuous maps acting on a compact metric space or by smooth maps on a compact Riemannian manifold. We also discuss a few examples to illustrate the sharpness of our estimates.<\/jats:p>","DOI":"10.1088\/1361-6544\/ac6b0d","type":"journal-article","created":{"date-parts":[[2022,6,8]],"date-time":"2022-06-08T08:20:26Z","timestamp":1654676426000},"page":"3159-3190","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Entropy inequalities for semigroup actions"],"prefix":"10.1088","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6929-6442","authenticated-orcid":true,"given":"Maria","family":"Carvalho","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7596-8214","authenticated-orcid":true,"given":"Fagner B","family":"Rodrigues","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0902-8718","authenticated-orcid":true,"given":"Paulo","family":"Varandas","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2022,5,26]]},"reference":[{"key":"nonac6b0dbib1a","first-page":"5","type":"journal-article","article-title":"Entropy of a skew product of mappings with invariant measure","volume":"17","author":"Abramov","year":"1962","journal-title":"Vestnik Leningrad. Univ."},{"key":"nonac6b0dbib1b","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1090\/trans2\/048\/12","type":"journal-article","article-title":"The entropy of a skew product of measure-preserving transformations","volume":"2","author":"Abramov","year":"1966","journal-title":"Am. Math. Soc. Transl. Ser."},{"key":"nonac6b0dbib2","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1007\/s002200050124","type":"journal-article","article-title":"Correlation spectrum of quenched and annealed equilibrium states for random expanding maps","volume":"186","author":"Baladi","year":"1997","journal-title":"Commun. Math. Phys."},{"key":"nonac6b0dbib3","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1007\/bf01188575","type":"journal-article","article-title":"A Margulis\u2013Ruelle inequality for random dynamical systems","volume":"64","author":"Bahnm\u00fcller","year":"1995","journal-title":"Arch. Math."},{"key":"nonac6b0dbib4","doi-asserted-by":"publisher","first-page":"639","DOI":"10.3934\/dcds.2004.11.639","type":"journal-article","article-title":"Entropies of a semigroup of maps","volume":"11","author":"Bi\u015b","year":"2004","journal-title":"Discrete Contin. Dyn. Syst."},{"key":"nonac6b0dbib5","doi-asserted-by":"publisher","first-page":"839","DOI":"10.5802\/aif.2778","type":"journal-article","article-title":"An analogue of the variational principle for group and pseudogroup actions","volume":"63","author":"Bi\u015b","year":"2013","journal-title":"Ann. Inst. Fourier"},{"key":"nonac6b0dbib6","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1007\/s10884-016-9554-2","type":"journal-article","article-title":"Topological and measure-theoretical entropies of nonautonomous dynamical systems","volume":"30","author":"Bi\u015b","year":"2018","journal-title":"J. Dyn. Differ. Equ."},{"article-title":"A convex analysis approach to entropy functions, variational principles and equilibrium states","year":"2020","author":"Bi\u015b","key":"nonac6b0dbib7","type":"preprint"},{"key":"nonac6b0dbib8","doi-asserted-by":"publisher","first-page":"131","DOI":"10.4064\/cm8017-12-2019","type":"journal-article","article-title":"Topological entropy, upper Carath\u00e9odory capacity and fractal dimensions of semigroup actions","volume":"163","author":"Bi\u015b","year":"2021","journal-title":"Colloq. Math."},{"key":"nonac6b0dbib9","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0097526","type":"book","article-title":"The Abramov\u2013Rokhlin formula","author":"Bogensch\u00fctz","year":"1992"},{"year":"1975","author":"Bowen","key":"nonac6b0dbib10","type":"book"},{"key":"nonac6b0dbib11","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1090\/s0002-9947-1971-0282372-0","type":"journal-article","article-title":"Periodic points and measures for axiom A diffeomorphisms","volume":"154","author":"Bowen","year":"1971","journal-title":"Trans. Am. Math. Soc."},{"key":"nonac6b0dbib12","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1080\/17476939908815193","type":"journal-article","article-title":"An invariant measure for finitely generated rational semigroups","volume":"39","author":"Boyd","year":"1999","journal-title":"Complex Var. Theory Appl. An Int. J."},{"key":"nonac6b0dbib13","first-page":"30","type":"book","article-title":"On local entropy","author":"Brin","year":"1983"},{"key":"nonac6b0dbib14","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1023\/A:1021796818247","type":"journal-article","article-title":"Topological entropy of free semigroup actions and skew-product transformations","volume":"5","author":"Bufetov","year":"1999","journal-title":"J. Dyn. Control Syst."},{"key":"nonac6b0dbib15","doi-asserted-by":"publisher","first-page":"1123","DOI":"10.1016\/j.jmaa.2015.09.042","type":"journal-article","article-title":"(Semi)continuity of the entropy of Sinai probability measures for partially hyperbolic diffeomorphisms","volume":"434","author":"Carvalho","year":"2016","journal-title":"J. Math. Anal. Appl."},{"key":"nonac6b0dbib16","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1007\/s10955-016-1697-3","type":"journal-article","article-title":"Semigroup actions of expanding maps","volume":"166","author":"Carvalho","year":"2017","journal-title":"J. Stat. Phys."},{"key":"nonac6b0dbib17","doi-asserted-by":"publisher","first-page":"3100","DOI":"10.3390\/e15083100","type":"journal-article","article-title":"On the topological entropy of some skew-product maps","volume":"15","author":"C\u00e1novas","year":"2013","journal-title":"Entropy"},{"key":"nonac6b0dbib18","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1016\/j.aim.2018.06.010","type":"journal-article","article-title":"A variational principle for free semigroup actions","volume":"334","author":"Carvalho","year":"2018","journal-title":"Adv. Math."},{"key":"nonac6b0dbib19","doi-asserted-by":"publisher","first-page":"1068","DOI":"10.1007\/bf02871841","type":"journal-article","article-title":"Some relations between Hausdorff-dimensions and entropies","volume":"41","author":"Dai","year":"1998","journal-title":"Sci. China A"},{"key":"nonac6b0dbib20","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1006\/aima.1999.1843","type":"journal-article","article-title":"Gibbs measures for fibred systems","volume":"148","author":"Denker","year":"1999","journal-title":"Adv. Math."},{"key":"nonac6b0dbib21","doi-asserted-by":"publisher","first-page":"525","DOI":"10.1016\/j.jmaa.2009.09.039","type":"journal-article","article-title":"Pointwise Lipschitz functions on metric spaces","volume":"363","author":"Durand-Cartagena","year":"2010","journal-title":"J. Math. Anal. Appl."},{"key":"nonac6b0dbib22","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/bf02125125","type":"journal-article","article-title":"Expansiveness, hyperbolicity and Hausdorff dimension","volume":"126","author":"Fathi","year":"1989","journal-title":"Commun. Math. Phys."},{"key":"nonac6b0dbib23","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/bf02392274","type":"journal-article","article-title":"Entropie g\u00e9om\u00e9trique des feuilletages","volume":"160","author":"Ghys","year":"1988","journal-title":"Acta Math."},{"year":"1986","author":"Kifer","key":"nonac6b0dbib24","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9175-3Birkh\u00e4user","type":"book"},{"key":"nonac6b0dbib25","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1023\/a:1025770720803","type":"journal-article","article-title":"Random versus deterministic exponents in a rich family of diffeomorphisms","volume":"113","author":"Ledrappier","year":"2003","journal-title":"J. Stat. Phys."},{"key":"nonac6b0dbib26","doi-asserted-by":"publisher","first-page":"509","DOI":"10.2307\/1971328","type":"journal-article","article-title":"The metric entropy of diffeomorphisms: I. Characterization of measures satisfying Pesin\u2019s entropy formula","volume":"122","author":"Ledrappier","year":"1985","journal-title":"Ann. Math."},{"key":"nonac6b0dbib27","doi-asserted-by":"publisher","first-page":"1279","DOI":"10.1017\/s0143385701001614","type":"journal-article","article-title":"Dynamics of random transformations: smooth ergodic theory","volume":"21","author":"Liu","year":"2001","journal-title":"Ergod. Theor. Dynam. Syst."},{"year":"1995","author":"Liu","key":"nonac6b0dbib28","type":"book"},{"key":"nonac6b0dbib29","doi-asserted-by":"publisher","first-page":"3751","DOI":"10.1090\/s0002-9947-06-03933-x","type":"journal-article","article-title":"Dimension of hyperbolic measures of random diffeomorphisms","volume":"358","author":"Liu","year":"2006","journal-title":"Trans. Am. Math. Soc."},{"key":"nonac6b0dbib30","first-page":"573","type":"journal-article","article-title":"Topological entropy and degree of smooth mappings","volume":"25","author":"Misiurewicz","year":"1977","journal-title":"Bull. Acad. Polon. Sci."},{"key":"nonac6b0dbib31","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1017\/s0004972717000703","type":"journal-article","article-title":"Lyapunov exponents on metric spaces","volume":"97","author":"Morales","year":"2018","journal-title":"Bull. Aust. Math. Soc."},{"key":"nonac6b0dbib32","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1109\/18.179344","type":"journal-article","article-title":"Entropy and data compression schemes","volume":"39","author":"Ornstein","year":"1993","journal-title":"IEEE Trans. Inform. Theory"},{"key":"nonac6b0dbib33","first-page":"197","type":"journal-article","article-title":"A multiplicative ergodic theorem. Characteristic Lyapunov exponents for dynamical systems","volume":"19","author":"Oseledets","year":"1968","journal-title":"Trans. Moscow Math. Soc."},{"key":"nonac6b0dbib34","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1070\/rm1977v032n04abeh001639","type":"journal-article","article-title":"Characteristic Lyapunov exponents and smooth ergodic theory","volume":"32","author":"Pesin","year":"1977","journal-title":"Russ. Math. Surv."},{"key":"nonac6b0dbib35","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1007\/bf01453234","type":"journal-article","article-title":"An upper estimation for topological entropy of diffeomorphisms","volume":"59","author":"Przytycki","year":"1980","journal-title":"Invent. Math."},{"year":"2010","author":"Przytycki","key":"nonac6b0dbib36","type":"book"},{"key":"nonac6b0dbib37","doi-asserted-by":"publisher","DOI":"10.1063\/1.4950928","type":"journal-article","article-title":"Specification and thermodynamical properties of semigroup actions","volume":"57","author":"Rodrigues","year":"2016","journal-title":"J. Math. Phys."},{"key":"nonac6b0dbib38","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/bf02584795","type":"journal-article","article-title":"An inequality for the entropy of differentiable maps","volume":"9","author":"Ruelle","year":"1978","journal-title":"Bol. Soc. Bras. Mat."},{"key":"nonac6b0dbib39","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1007\/s00220-021-04088-w","type":"journal-article","article-title":"Thermodynamic formalism for random non-uniformly expanding maps","volume":"385","author":"Stadlbauer","year":"2021","journal-title":"Commun. Math. Phys."},{"article-title":"Quenched and annealed equilibrium states for random Ruelle expanding maps and applications","year":"2020","author":"Stadlbauer","key":"nonac6b0dbib40","type":"preprint"},{"key":"nonac6b0dbib41","doi-asserted-by":"publisher","first-page":"1350015","DOI":"10.1142\/s0219493713500159","type":"journal-article","article-title":"Relative equilibrium states and dimensions of fiberwise invariant measures for random distance expanding maps","volume":"14","author":"Simmons","year":"2014","journal-title":"Stochast. Dynam."},{"key":"nonac6b0dbib42","doi-asserted-by":"publisher","first-page":"995","DOI":"10.1088\/0951-7715\/13\/4\/302","type":"journal-article","article-title":"Skew product maps related to finitely generated rational semigroups","volume":"13","author":"Sumi","year":"2000","journal-title":"Nonlinearity"},{"year":"1975","author":"Walters","key":"nonac6b0dbib43","type":"book"},{"key":"nonac6b0dbib44","doi-asserted-by":"publisher","first-page":"1573","DOI":"10.1016\/j.jmaa.2015.11.038","type":"journal-article","article-title":"On the topological entropy of free semigroup actions","volume":"435","author":"Wang","year":"2016","journal-title":"J. Math. Anal. Appl."},{"key":"nonac6b0dbib45","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-021-10055-9","type":"journal-article","article-title":"Topological pressure of free semigroup sections for non-compact sets and Bowen\u2019s equation I","author":"Xiao","year":"2021","journal-title":"J. Dyn. Differ. Equ."},{"key":"nonac6b0dbib46","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/bf01453235","type":"journal-article","article-title":"A remark on the topological entropy of homeomorphisms","volume":"59","author":"Yano","year":"1980","journal-title":"Invent. Math."},{"key":"nonac6b0dbib47","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1017\/s0143385700009615","type":"journal-article","article-title":"Dimension, entropy and Lyapunov exponents","volume":"2","author":"Young","year":"1982","journal-title":"Ergod. Theor. Dynam. Syst."},{"key":"nonac6b0dbib48","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1142\/s0219493708002275","type":"journal-article","article-title":"On local entropy of random transformations","volume":"08","author":"Zhu","year":"2008","journal-title":"Stochast. Dynam."}],"container-title":["Nonlinearity"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ac6b0d","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ac6b0d\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ac6b0d\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ac6b0d\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T11:31:23Z","timestamp":1760787083000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ac6b0d"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,26]]},"references-count":49,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,5,26]]},"published-print":{"date-parts":[[2022,6,6]]}},"URL":"https:\/\/doi.org\/10.1088\/1361-6544\/ac6b0d","relation":{},"ISSN":["0951-7715","1361-6544"],"issn-type":[{"type":"print","value":"0951-7715"},{"type":"electronic","value":"1361-6544"}],"subject":[],"published":{"date-parts":[[2022,5,26]]},"assertion":[{"value":"Entropy inequalities for semigroup actions","name":"article_title","label":"Article Title"},{"value":"Nonlinearity","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2022 IOP Publishing Ltd & London Mathematical Society. All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2021-08-04","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2022-04-27","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2022-05-26","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}