{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T22:57:49Z","timestamp":1649113069391},"reference-count":10,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T00:00:00Z","timestamp":1605571200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"FCT\/Portugal","award":["UID\/MAT\/04459\/2019"],"award-info":[{"award-number":["UID\/MAT\/04459\/2019"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,12,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>For a linear impulsive differential equation, we introduce a Lyapunov regularity coefficient following as far as possible the non-impulsive case. We recall that a regularity coefficient is a quantity that characterizes the Lyapunov regularity of the dynamics. In particular, we obtain lower and upper bounds for the Lyapunov regularity coefficient and we show that its computation can always be reduced to that of the corresponding coefficient of an impulsive dynamics defined by upper triangular matrices. We also relate the Lyapunov regularity coefficient with the Grobman regularity coefficient. Finally, we combine all the former results to establish a criterion for tempered exponential behavior in terms of the Lyapunov exponents and of the Lyapunov regularity coefficient.<\/jats:p>","DOI":"10.1093\/qmath\/haaa048","type":"journal-article","created":{"date-parts":[[2020,10,6]],"date-time":"2020-10-06T11:19:43Z","timestamp":1601983183000},"page":"1535-1556","source":"Crossref","is-referenced-by-count":0,"title":["Regularity Coefficients for Impulsive Differential Equations"],"prefix":"10.1093","volume":"71","author":[{"given":"Luis","family":"Barreira","sequence":"first","affiliation":[{"name":"Center for Mathematical Analysis, Geometry and Dynamical Systems, Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]},{"given":"Claudia","family":"Valls","sequence":"additional","affiliation":[{"name":"Center for Mathematical Analysis, Geometry and Dynamical Systems, Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]}],"member":"286","published-online":{"date-parts":[[2020,11,17]]},"reference":[{"key":"2020122309100562900_R1","volume-title":"Lyapunov Exponents and Smooth Ergodic Theory","author":"Barreira","year":"2002"},{"key":"2020122309100562900_R2","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-74775-8","volume-title":"Stability of Nonautonomous Differential Equations","author":"Barreira","year":"2008"},{"key":"2020122309100562900_R3","doi-asserted-by":"crossref","first-page":"1596","DOI":"10.1016\/j.jde.2010.07.016","article-title":"Lyapunov regularity of impulsive differential equations","volume":"249","author":"Barreira","year":"2010","journal-title":"J. Differential Equations"},{"key":"2020122309100562900_R4","doi-asserted-by":"crossref","DOI":"10.1515\/9783110295313","volume-title":"Impulsive Differential Inclusions. A Fixed Point Approach","author":"Graef","year":"2013"},{"key":"2020122309100562900_R5","doi-asserted-by":"crossref","DOI":"10.1515\/9781400865246","volume-title":"Impulsive and Hybrid Dynamical Systems. Stability, Dissipativity, and Control","author":"Haddad","year":"2006"},{"key":"2020122309100562900_R6","doi-asserted-by":"crossref","DOI":"10.1142\/0906","volume-title":"Theory of Impulsive Differential Equations","author":"Lakshmikantham","year":"1989"},{"key":"2020122309100562900_R7","volume-title":"Switched and Impulsive Systems. Analysis, Design, and Applications","author":"Li","year":"2005"},{"key":"2020122309100562900_R8","doi-asserted-by":"crossref","DOI":"10.1080\/00207179208934253","volume-title":"The General Problem of the Stability of Motion","author":"Lyapunov","year":"1992"},{"key":"2020122309100562900_R9","doi-asserted-by":"crossref","volume-title":"Impulsive Differential Equations","author":"Samoilenko","DOI":"10.1142\/2892"},{"key":"2020122309100562900_R10","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-28061-5","volume-title":"Applied Impulsive Mathematical Models","author":"Stamova","year":"2016"}],"container-title":["The Quarterly Journal of Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/qjmath\/article-pdf\/71\/4\/1535\/35093205\/haaa048.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/qjmath\/article-pdf\/71\/4\/1535\/35093205\/haaa048.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,23]],"date-time":"2020-12-23T15:07:14Z","timestamp":1608736034000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/qjmath\/article\/71\/4\/1535\/5985569"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,17]]},"references-count":10,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,11,17]]},"published-print":{"date-parts":[[2020,12,11]]}},"URL":"https:\/\/doi.org\/10.1093\/qmath\/haaa048","relation":{},"ISSN":["0033-5606","1464-3847"],"issn-type":[{"value":"0033-5606","type":"print"},{"value":"1464-3847","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,12,1]]},"published":{"date-parts":[[2020,11,17]]}}}