{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,9]],"date-time":"2025-11-09T07:38:02Z","timestamp":1762673882811},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2012,6,20]],"date-time":"2012-06-20T00:00:00Z","timestamp":1340150400000},"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":[[2012,7]]},"DOI":"10.1007\/s10955-012-0524-8","type":"journal-article","created":{"date-parts":[[2012,6,19]],"date-time":"2012-06-19T16:30:15Z","timestamp":1340123415000},"page":"137-163","source":"Crossref","is-referenced-by-count":8,"title":["Lyapunov Functions and Cone Families"],"prefix":"10.1007","volume":"148","author":[{"given":"Luis","family":"Barreira","sequence":"first","affiliation":[]},{"given":"Davor","family":"Dragi\u010devi\u0107","sequence":"additional","affiliation":[]},{"given":"Claudia","family":"Valls","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,6,20]]},"reference":[{"key":"524_CR1","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1070\/SM1968v005n01ABEH002587","volume":"5","author":"V. Alekseev","year":"1968","unstructured":"Alekseev, V.: Quasirandom dynamical systems. I. Quasirandom diffeomorphisms. Math. USSR Sb. 5, 73\u2013128 (1968)","journal-title":"Math. USSR Sb."},{"key":"524_CR2","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1070\/SM1968v006n04ABEH001074","volume":"6","author":"V. Alekseev","year":"1968","unstructured":"Alekseev, V.: Quasirandom dynamical systems. II. One-dimensional nonlinear vibrations in a periodically perturbed field. Math. USSR Sb. 6, 505\u2013560 (1968)","journal-title":"Math. USSR Sb."},{"key":"524_CR3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1070\/SM1969v007n01ABEH001076","volume":"7","author":"V. Alekseev","year":"1969","unstructured":"Alekseev, V.: Quasirandom dynamical systems. III. Quasirandom vibrations of one-dimensional oscillators. Math. USSR Sb. 7, 1\u201343 (1969)","journal-title":"Math. USSR Sb."},{"key":"524_CR4","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/S1874-575X(06)80027-5","volume-title":"Handbook of Dynamical Systems 1B","author":"L. Barreira","year":"2006","unstructured":"Barreira, L., Pesin, Ya.: Smooth ergodic theory and nonuniformly hyperbolic dynamics, with an appendix by O. Sarig. In: Hasselblatt, B., Katok, A. (eds.) Handbook of Dynamical Systems 1B, pp. 57\u2013263. Elsevier, Amsterdam (2006)"},{"key":"524_CR5","series-title":"Encyclopedia of Math. and Its Appl.","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 Math. and Its Appl., vol. 115. Cambridge University Press, Cambridge (2007)"},{"key":"524_CR6","doi-asserted-by":"crossref","first-page":"4743","DOI":"10.1016\/j.jde.2009.01.020","volume":"246","author":"L. Barreira","year":"2009","unstructured":"Barreira, L., Valls, C.: Nonuniform exponential contractions and Lyapunov sequences. J. Differ. Equ. 246, 4743\u20134771 (2009)","journal-title":"J. Differ. Equ."},{"key":"524_CR7","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1070\/SM1973v019n03ABEH001786","volume":"19","author":"L. Bunimovich","year":"1974","unstructured":"Bunimovich, L., Sinai, Ya.: On a fundamental theorem in the theory of dispersing billiards. Math. USSR Sb. 19, 407\u2013423 (1974)","journal-title":"Math. USSR Sb."},{"key":"524_CR8","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.\u00a0Stat. Phys. 108, 927\u2013942 (2002)","journal-title":"J.\u00a0Stat. Phys."},{"key":"524_CR9","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":"524_CR10","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. 127. Am. Math. Soc., Providence (2006)"},{"key":"524_CR11","series-title":"Mem. Am. Math. Soc.","volume-title":"Conditional Stability and Real Analytic Pseudo-Anosov Maps","author":"M. Gerber","year":"1985","unstructured":"Gerber, M.: Conditional Stability and Real Analytic Pseudo-Anosov Maps. Mem. Am. Math. Soc., vol.\u00a055, Nr. 321 (1985)"},{"key":"524_CR12","doi-asserted-by":"crossref","first-page":"173","DOI":"10.24033\/asens.1424","volume":"15","author":"M. Gerber","year":"1982","unstructured":"Gerber, M., Katok, A.: Smooth models of Thurston\u2019s pseudo-Anosov maps. Ann. Sci. \u00c9c. Norm. Super.\u00a0(4) 15, 173\u2013204 (1982)","journal-title":"Ann. Sci. \u00c9c. Norm. Super.\u00a0(4)"},{"key":"524_CR13","doi-asserted-by":"crossref","first-page":"529","DOI":"10.2307\/1971237","volume":"110","author":"A. Katok","year":"1979","unstructured":"Katok, A.: Bernoulli diffeomorphisms on surfaces. Ann. Math. (2) 110, 529\u2013547 (1979)","journal-title":"Ann. Math. (2)"},{"key":"524_CR14","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1017\/S0143385700008142","volume":"14","author":"A. Katok","year":"1994","unstructured":"Katok, A., Burns, K.: Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dynamical systems. Ergod. Theory Dyn. Syst. 14, 757\u2013785 (1994)","journal-title":"Ergod. Theory Dyn. Syst."},{"key":"524_CR15","series-title":"Lect. Notes. in Math.","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0099031","volume-title":"Invariant Manifolds, Entropy and Billiards; Smooth Maps with Singularities","author":"A. Katok","year":"1986","unstructured":"Katok, A., Strelcyn, J.-M. (with the collaboration of F. Ledrappier, F. Przytycki): Invariant Manifolds, Entropy and Billiards; Smooth Maps with Singularities. Lect. Notes. in Math., vol. 1222. Springer, Berlin (1986)."},{"key":"524_CR16","doi-asserted-by":"crossref","DOI":"10.1515\/9783110844641","volume-title":"Ergodic Theorems","author":"U. Krengel","year":"1985","unstructured":"Krengel, U.: Ergodic Theorems. de Gruyter, Berlin (1985)"},{"key":"524_CR17","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/0022-0396(80)90004-2","volume":"38","author":"J. Lewowicz","year":"1980","unstructured":"Lewowicz, J.: Lyapunov functions and topological stability. J. Differ. Equ. 38, 192\u2013209 (1980)","journal-title":"J. Differ. Equ."},{"key":"524_CR18","series-title":"Lect. Notes. in Math.","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1007\/BFb0061429","volume-title":"Geometric Dynamics","author":"J. Lewowicz","year":"1983","unstructured":"Lewowicz, J.: Lyapunov functions and stability of geodesic flows. In: Palis, J. (ed.) Geometric Dynamics, Rio de Janeiro, 1981. Lect. Notes. in Math., vol. 1007, pp. 463\u2013479. Springer, Berlin (1983)"},{"key":"524_CR19","doi-asserted-by":"crossref","first-page":"339","DOI":"10.2140\/pjm.1994.166.339","volume":"166","author":"C. Liverani","year":"1994","unstructured":"Liverani, C., Wojtkowski, M.: Generalization of the Hilbert metric to the space of positive definite matrices. Pac. J. Math. 166, 339\u2013355 (1994)","journal-title":"Pac. J. Math."},{"key":"524_CR20","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1007\/978-3-642-61215-2_3","volume-title":"Dynamics Reported Expositions in Dynamical. Systems 4","author":"C. Liverani","year":"1995","unstructured":"Liverani, C., Wojtkowski, M.: Ergodicity in Hamiltonian systems. In: Dynamics Reported Expositions in Dynamical. Systems 4, pp. 130\u2013202. Springer, Berlin (1995)"},{"key":"524_CR21","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.5802\/afst.779","volume":"3","author":"R. Markarian","year":"1994","unstructured":"Markarian, R.: Non-uniformly hyperbolic billiards. Ann. Fac. Sci. Toulouse 3, 1207\u20131239 (1994)","journal-title":"Ann. Fac. Sci. Toulouse"},{"key":"524_CR22","first-page":"197","volume":"19","author":"V. Oseledets","year":"1968","unstructured":"Oseledets, V.: A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Trans. Mosc. Math. Soc. 19, 197\u2013221 (1968)","journal-title":"Trans. Mosc. Math. Soc."},{"key":"524_CR23","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 corresponding to nonzero characteristic exponents. Math. USSR, Izv. 10, 1261\u20131305 (1976)","journal-title":"Math. USSR, Izv."},{"key":"524_CR24","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1070\/RM1977v032n04ABEH001639","volume":"32","author":"Ya. Pesin","year":"1977","unstructured":"Pesin, Ya.: Characteristic Lyapunov exponents, and smooth ergodic theory. Russ. Math. Surv. 32, 55\u2013114 (1977)","journal-title":"Russ. Math. Surv."},{"key":"524_CR25","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1070\/IM1977v011n06ABEH001766","volume":"11","author":"Ya. Pesin","year":"1977","unstructured":"Pesin, Ya.: Geodesic flows on closed Riemannian manifolds without focal points. Math. USSR, Izv. 11, 1195\u20131228 (1977)","journal-title":"Math. USSR, Izv."},{"key":"524_CR26","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1090\/trans2\/015\/07","volume":"15","author":"V. Potapov","year":"1960","unstructured":"Potapov, V.: The multiplicative structure of J-contractive matrix functions. Transl. Am. Math. Soc. 15, 131\u2013243 (1960)","journal-title":"Transl. Am. Math. Soc."},{"key":"524_CR27","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1090\/trans2\/138\/04","volume":"138","author":"V. Potapov","year":"1988","unstructured":"Potapov, V.: Linear fractional transformation of matrices. Transl. Am. Math. Soc. 138, 21\u201335 (1988)","journal-title":"Transl. Am. Math. Soc."},{"key":"524_CR28","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1090\/trans2\/138\/06","volume":"138","author":"V. Potapov","year":"1988","unstructured":"Potapov, V.: A theorem on the modulus. I. Transl. Am. Math. Soc. 138, 55\u201365 (1988)","journal-title":"Transl. Am. Math. Soc."},{"key":"524_CR29","first-page":"124","volume-title":"Statistical Irreversibility in Nonlinear Systems","author":"Ya. Sinai","year":"1970","unstructured":"Sinai, Ya.: Some rigorous results on decay of correlations. In: Zaslavskij, G. (ed.) Statistical Irreversibility in Nonlinear Systems, supplement to the book, pp. 124\u2013139. Nauka, Moscow (1970)"},{"key":"524_CR30","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1070\/RM1987v042n03ABEH001421","volume":"42","author":"Ya. Sinai","year":"1987","unstructured":"Sinai, Ya., Chernov, N.: Ergodic properties of certain systems of two-dimensional discs and three-dimensional balls. Russ. Math. Surv. 42, 181\u2013207 (1987)","journal-title":"Russ. Math. Surv."},{"key":"524_CR31","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.1016\/S0764-4442(99)80439-X","volume":"328","author":"W. Tucker","year":"1999","unstructured":"Tucker, W.: The Lorenz attractor exists. C. R. Acad. Sci. Paris, S\u00e9r. I Math. 328, 1197\u20131202 (1999)","journal-title":"C. R. Acad. Sci. Paris, S\u00e9r. I Math."},{"key":"524_CR32","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1017\/S0143385700002807","volume":"5","author":"M. Wojtkowski","year":"1985","unstructured":"Wojtkowski, M.: Invariant families of cones and Lyapunov exponents. Ergod. Theory Dyn. Syst. 5, 145\u2013161 (1985)","journal-title":"Ergod. Theory Dyn. Syst."},{"key":"524_CR33","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1017\/S0143385700004363","volume":"8","author":"M. Wojtkowski","year":"1988","unstructured":"Wojtkowski, M.: Measure theoretic entropy of the system of hard spheres. Ergod. Theory Dyn. Syst. 8, 133\u2013153 (1988)","journal-title":"Ergod. Theory Dyn. Syst."},{"key":"524_CR34","series-title":"Lect. Notes in Math.","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1007\/BFb0086674","volume-title":"Lyapunov Exponents","author":"M. Wojtkowski","year":"1991","unstructured":"Wojtkowski, M.: Systems of classical interacting particles with nonvanishing Lyapunov exponents. In: Arnold, L., Crauel, H., Eckmann, J.-P. (eds.) Lyapunov Exponents, Oberwolfach, 1990. Lect. Notes in Math., vol. 1486, pp. 243\u2013262. Springer, Berlin (1991)"},{"key":"524_CR35","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1016\/S0021-7824(00)00176-8","volume":"79","author":"M. Wojtkowski","year":"2000","unstructured":"Wojtkowski, M.: W-flows on Weyl manifolds and Gaussian thermostats. J. Math. Pures Appl. (9) 79, 953\u2013974 (2000)","journal-title":"J. Math. Pures Appl. (9)"},{"key":"524_CR36","doi-asserted-by":"crossref","first-page":"177","DOI":"10.4064\/fm-163-2-177-191","volume":"163","author":"M. Wojtkowski","year":"2000","unstructured":"Wojtkowski, M.: Magnetic flows and Gaussian thermostats on manifolds of negative curvature. Fundam. Math. 163, 177\u2013191 (2000)","journal-title":"Fundam. Math."},{"key":"524_CR37","series-title":"Proc. Sympos. Pure Math.","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1090\/pspum\/069\/1858544","volume-title":"Smooth Ergodic Theory and Its Applications","author":"M. Wojtkowski","year":"2001","unstructured":"Wojtkowski, M.: Monotonicity, J-algebra of Potapov and Lyapunov exponents. In: Smooth Ergodic Theory and Its Applications, Seattle, 1999. Proc. Sympos. Pure Math., vol. 69, pp. 499\u2013521. Am. Math. Soc., Providence (2001)"}],"container-title":["Journal of Statistical Physics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10955-012-0524-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10955-012-0524-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10955-012-0524-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,30]],"date-time":"2019-06-30T03:37:33Z","timestamp":1561865853000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10955-012-0524-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,20]]},"references-count":37,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,7]]}},"alternative-id":["524"],"URL":"https:\/\/doi.org\/10.1007\/s10955-012-0524-8","relation":{},"ISSN":["0022-4715","1572-9613"],"issn-type":[{"value":"0022-4715","type":"print"},{"value":"1572-9613","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,20]]}}}