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Then, we prove the existence of a generalized Liouville Formula for conformally symplectic systems with rigid constraints using the integral invariant. A two degree-of-freedom system is analyzed to support the relevance of our results. <\/jats:p>","DOI":"10.1142\/s0218127421502175","type":"journal-article","created":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T13:10:48Z","timestamp":1637673048000},"source":"Crossref","is-referenced-by-count":1,"title":["Dynamics of Dissipative Systems with Hamiltonian Structures"],"prefix":"10.1142","volume":"31","author":[{"given":"Xiaoming","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, P. R. China"}]},{"given":"Zhenbang","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, P. R. China"}]},{"given":"Jianhua","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, P. R. China"}]},{"given":"Denghui","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Hexi University, Zhangye, Gansu 734000, P. R. China"}]},{"given":"Celso","family":"Grebogi","sequence":"additional","affiliation":[{"name":"Institute for Complex Systems and Mathematical Biology, King\u2019s College, University of Aberdeen, Aberdeen, AB24 3UE, UK"}]}],"member":"219","published-online":{"date-parts":[[2021,11,23]]},"reference":[{"key":"S0218127421502175BIB001","doi-asserted-by":"publisher","DOI":"10.1063\/1.166039"},{"key":"S0218127421502175BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2063-1"},{"volume-title":"Piecewise-Smooth Dynamical Systems: Theory and Applications","year":"2009","author":"Bernardo M. di","key":"S0218127421502175BIB003"},{"key":"S0218127421502175BIB004","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1995.0329"},{"key":"S0218127421502175BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2013.05.001"},{"key":"S0218127421502175BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-013-9319-0"},{"key":"S0218127421502175BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(88)90036-X"},{"key":"S0218127421502175BIB008","unstructured":"Chenciner, A.   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