{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T02:49:21Z","timestamp":1761014961635},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2010,8,18]],"date-time":"2010-08-18T00:00:00Z","timestamp":1282089600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Stat Phys"],"published-print":{"date-parts":[[2010,10]]},"DOI":"10.1007\/s10955-010-0043-4","type":"journal-article","created":{"date-parts":[[2010,8,17]],"date-time":"2010-08-17T13:34:50Z","timestamp":1282052090000},"page":"179-200","source":"Crossref","is-referenced-by-count":10,"title":["Invariant Manifolds for Impulsive Equations and\u00a0Nonuniform Polynomial Dichotomies"],"prefix":"10.1007","volume":"141","author":[{"given":"Luis","family":"Barreira","sequence":"first","affiliation":[]},{"given":"Meng","family":"Fan","sequence":"additional","affiliation":[]},{"given":"Claudia","family":"Valls","sequence":"additional","affiliation":[]},{"given":"Jimin","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,8,18]]},"reference":[{"key":"43_CR1","volume-title":"Impulsive Differential Equations: Periodic Solutions and Applications","author":"D. Bainov","year":"1993","unstructured":"Bainov, D., Simeonov, P.: Impulsive Differential Equations: Periodic Solutions and Applications. Longman, Harlow (1993)"},{"key":"43_CR2","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1007\/BF00669823","volume":"28","author":"D. Bainov","year":"1989","unstructured":"Bainov, D., Kostadinov, S., Zabreiko, P.: Exponential dichotomy of linear impulsive differential equations in a Banach space. Int. J. Theor. Phys. 28, 797\u2013814 (1989)","journal-title":"Int. J. Theor. Phys."},{"key":"43_CR3","series-title":"University Lecture Series","volume-title":"Lyapunov Exponents and Smooth Ergodic Theory","author":"L. Barreira","year":"2002","unstructured":"Barreira, L., Pesin, Ya.: Lyapunov Exponents and Smooth Ergodic Theory. University Lecture Series, vol.\u00a023. American Mathematical Society, Providence (2002)"},{"key":"43_CR4","doi-asserted-by":"crossref","unstructured":"Barreira, L., Pesin, Ya.: Smooth ergodic theory and nonuniformly hyperbolic dynamics, with an appendix by O. Sarig. Handbook of Dynamical Systems, vol.\u00a01B. pp. 57\u2013263 Elsevier, Amsterdam (2006)","DOI":"10.1016\/S1874-575X(06)80027-5"},{"key":"43_CR5","series-title":"Encyclopedia of Mathematics and Its Applications","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781107326026","volume-title":"Nonuniform Hyperbolicity","author":"L. Barreira","year":"2007","unstructured":"Barreira, L., Pesin, Ya.: Nonuniform Hyperbolicity. Encyclopedia of Mathematics and Its Applications, vol.\u00a0115. Cambridge University Press, Cambridge (2007)"},{"key":"43_CR6","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-74775-8","volume-title":"Stability of Nonautonomous Differential Equations","author":"L. Barreira","year":"2008","unstructured":"Barreira, L., Valls, C.: Stability of Nonautonomous Differential Equations. Lecture Notes in Mathematics, vol.\u00a01926. Springer, Berlin (2008)"},{"key":"43_CR7","doi-asserted-by":"crossref","first-page":"5208","DOI":"10.1016\/j.na.2009.04.005","volume":"71","author":"L. Barreira","year":"2009","unstructured":"Barreira, L., Valls, C.: Polynomial growth rates. Nonlinear Anal. 71, 5208\u20135219 (2009)","journal-title":"Nonlinear Anal."},{"key":"43_CR8","doi-asserted-by":"crossref","unstructured":"Barreira, L., Valls, C.: Stable manifolds for impulsive equations under nonuniform hyperbolicity, J. Dyn. Differ. Equ. (to appear)","DOI":"10.1007\/s10884-010-9161-6"},{"key":"43_CR9","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.jfa.2009.01.032","volume":"257","author":"A. Bento","year":"2009","unstructured":"Bento, A., Silva, C.: Stable manifolds for nonuniform polynomial dichotomies. J. Funct. Anal. 257, 122\u2013148 (2009)","journal-title":"J. Funct. Anal."},{"key":"43_CR10","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1023\/A:1019779128351","volume":"108","author":"K. Burns","year":"2002","unstructured":"Burns, K., Dolgopyat, D., Pesin, Ya.: Partial hyperbolicity, Lyapunov exponents and stable ergodicity. J. Stat. Phys. 108, 927\u2013942 (2002)","journal-title":"J. Stat. Phys."},{"key":"43_CR11","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1023\/A:1004581304939","volume":"94","author":"N. Chernov","year":"1999","unstructured":"Chernov, N.: Decay of correlations and dispersing billiards. J. Stat. Phys. 94, 513\u2013556 (1999)","journal-title":"J. Stat. Phys."},{"key":"43_CR12","series-title":"Mathematical Surveys and Monographs","doi-asserted-by":"crossref","DOI":"10.1090\/surv\/127","volume-title":"Chaotic Billiards","author":"N. Chernov","year":"2006","unstructured":"Chernov, N., Markarian, R.: Chaotic Billiards. Mathematical Surveys and Monographs, vol.\u00a0127. Amer. Math. Soc., Providence (2006)"},{"key":"43_CR13","doi-asserted-by":"crossref","unstructured":"Katok, A., Strelcyn, J.-M.: Invariant Manifolds, Entropy and Billiards; Smooth Maps with Singularities, with the collaboration of F. Ledrappier and F. Przytycki. Lecture Notes in Mathematics, vol.\u00a01222. Springer (1986)","DOI":"10.1007\/BFb0099031"},{"key":"43_CR14","doi-asserted-by":"crossref","DOI":"10.1142\/0906","volume-title":"Theory of Impulsive Differential Equations","author":"V. Lakshmikanthan","year":"1989","unstructured":"Lakshmikanthan, V., Bainov, D., Simeonov, P.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)"},{"key":"43_CR15","first-page":"197","volume":"19","author":"V. Oseledets","year":"1968","unstructured":"Oseledets, V.: A multiplicative ergodic theorem. Liapunov characteristic numbers for dynamical systems. Trans. Mosc. Math. Soc. 19, 197\u2013221 (1968)","journal-title":"Trans. Mosc. Math. Soc."},{"key":"43_CR16","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1007\/BF01194662","volume":"32","author":"O. Perron","year":"1930","unstructured":"Perron, O.: Die Stabilit\u00e4tsfrage bei Differentialgleichungen. Math. Z. 32, 703\u2013728 (1930)","journal-title":"Math. Z."},{"key":"43_CR17","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1070\/IM1976v010n06ABEH001835","volume":"10","author":"Ya. Pesin","year":"1976","unstructured":"Pesin, Ya.: Families of invariant manifolds that corresponding to nonzero characteristic exponents. Math. USSR, Izv. 10, 1261\u20131305 (1976)","journal-title":"Math. USSR, Izv."},{"key":"43_CR18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0002-9947-1989-0983869-1","volume":"312","author":"C. Pugh","year":"1989","unstructured":"Pugh, C., Shub, M.: Ergodic attractors. Trans. Am. Math. Soc. 312, 1\u201354 (1989)","journal-title":"Trans. Am. Math. Soc."},{"key":"43_CR19","doi-asserted-by":"crossref","first-page":"243","DOI":"10.2307\/1971392","volume":"115","author":"D. Ruelle","year":"1982","unstructured":"Ruelle, D.: Characteristic exponents and invariant manifolds in Hilbert space. Ann. Math. 115, 243\u2013290 (1982)","journal-title":"Ann. Math."},{"key":"43_CR20","series-title":"Nonlinear Science Series A: Monographs and Treatises","doi-asserted-by":"crossref","DOI":"10.1142\/2892","volume-title":"Impulsive Differential Equations","author":"A. Samoilenko","year":"1995","unstructured":"Samoilenko, A., Perestyuk, N.: Impulsive Differential Equations, Nonlinear Science Series A: Monographs and Treatises, vol.\u00a014. World Scientific, River Edge (1995)"}],"container-title":["Journal of Statistical Physics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10955-010-0043-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10955-010-0043-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10955-010-0043-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T09:51:14Z","timestamp":1559469074000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10955-010-0043-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,8,18]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,10]]}},"alternative-id":["43"],"URL":"https:\/\/doi.org\/10.1007\/s10955-010-0043-4","relation":{},"ISSN":["0022-4715","1572-9613"],"issn-type":[{"value":"0022-4715","type":"print"},{"value":"1572-9613","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,8,18]]}}}