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Moreover, we study the convergence and Lipschitz regularity of the pressure function and obtain relations between topological entropy and exponential growth rate of periodic points in the context of semigroups of expanding maps, obtaining a partial extension of the results obtained by Ruelle for \u2124d-actions [D. Ruelle, Trans. Am. Math. Soc., 187, 237\u2013251 (1973)]. The specification properties for semigroup actions and the corresponding one for its generators and the action of push-forward maps are also discussed.<\/jats:p>","DOI":"10.1063\/1.4950928","type":"journal-article","created":{"date-parts":[[2016,5,25]],"date-time":"2016-05-25T02:28:35Z","timestamp":1464143315000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":44,"title":["Specification and thermodynamical properties of semigroup actions"],"prefix":"10.1063","volume":"57","author":[{"given":"Fagner B.","family":"Rodrigues","sequence":"first","affiliation":[{"name":"Universidade Federal do Rio Grande do Sul 1 Departamento de Matem\u00e1tica, , Rio Grande do Sul, Brazil"},{"name":"University of Porto 2 CMUP, , Porto, Portugal"}]},{"given":"Paulo","family":"Varandas","sequence":"additional","affiliation":[{"name":"University of Porto 2 CMUP, , Porto, Portugal"},{"name":"Universidade Federal da Bahia 3 Departamento de Matem\u00e1tica, , Av. 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