{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,28]],"date-time":"2026-07-28T06:20:56Z","timestamp":1785219656700,"version":"3.55.0"},"reference-count":40,"publisher":"AIP Publishing","issue":"8","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11775035"],"award-info":[{"award-number":["11775035"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2019XD-A10"],"award-info":[{"award-number":["2019XD-A10"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["92067202"],"award-info":[{"award-number":["92067202"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2022,8,1]]},"abstract":"<jats:p>As periodic orbit theory works badly on computing the observable averages of dynamical systems with intermittency, we propose a scheme to cooperate with cycle expansion and perturbation theory so that we can deal with intermittent systems and compute the averages more precisely. The periodic orbit theory assumes that the shortest unstable periodic orbits build the framework of the system and provide cycle expansion to compute dynamical quantities based on them, while the perturbation theory can locally analyze the structure of dynamical systems. The dynamical averages may be obtained more precisely by combining the two techniques together. Based on the integrability near the marginal orbits and the hyperbolicity in the part away from the singularities in intermittent systems, the chief idea of this paper is to revise intermittent maps and maintain the natural measure produced by the original maps. We get the natural measure near the singularity through the Taylor expansions, and the periodic orbit theory captures the natural measure in the other parts of the phase space. We try this method on one-dimensional intermittent maps with single singularity, and more precise results are achieved.<\/jats:p>","DOI":"10.1063\/5.0087463","type":"journal-article","created":{"date-parts":[[2022,8,10]],"date-time":"2022-08-10T14:51:05Z","timestamp":1660143065000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":4,"title":["Wielding intermittency with cycle expansions"],"prefix":"10.1063","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1506-1805","authenticated-orcid":false,"given":"Huanyu","family":"Cao","sequence":"first","affiliation":[{"name":"School of Science, Beijing University of Posts and Telecommunications 1 , Beijing 100876, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ang","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Science, Beijing University of Posts and Telecommunications 1 , Beijing 100876, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haotian","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Science, Beijing University of Posts and Telecommunications 1 , Beijing 100876, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2950-8022","authenticated-orcid":false,"given":"Yueheng","family":"Lan","sequence":"additional","affiliation":[{"name":"School of Science, Beijing University of Posts and Telecommunications 1 , Beijing 100876, China"},{"name":"State Key Lab of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications 2 , Beijing 100876, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2022,8,10]]},"reference":[{"key":"2023080922073594300_c1","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1088\/0951-7715\/3\/2\/005","article-title":"Recycling of strange sets: I. Cycle expansions","volume":"3","year":"1990","journal-title":"Nonlinearity"},{"key":"2023080922073594300_c2","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1016\/j.cnsns.2009.04.022","article-title":"Cycle expansions: From maps to turbulence","volume":"15","year":"2010","journal-title":"Commun. Nonlinear Sci."},{"key":"2023080922073594300_c3","volume-title":"Chaos II","year":"1990"},{"key":"2023080922073594300_c4"},{"key":"2023080922073594300_c5","doi-asserted-by":"publisher","first-page":"2387","DOI":"10.1103\/PhysRevLett.58.2387","article-title":"Exploring chaotic motion through periodic orbits","volume":"58","year":"1987","journal-title":"Phys. Rev. Lett."},{"key":"2023080922073594300_c6","doi-asserted-by":"publisher","first-page":"3936","DOI":"10.1103\/PhysRevE.60.3936","article-title":"Spectrum of stochastic evolution operators: Local matrix representation approach","volume":"60","year":"1999","journal-title":"Phys. Rev. E"},{"key":"2023080922073594300_c7","doi-asserted-by":"publisher","first-page":"L237","DOI":"10.1088\/0305-4470\/24\/5\/005","article-title":"Periodic orbit expansions for classical smooth flows","volume":"24","year":"1991","journal-title":"J. Phys. A"},{"key":"2023080922073594300_c8","doi-asserted-by":"publisher","first-page":"2729","DOI":"10.1103\/PhysRevLett.61.2729","article-title":"Invariant measurement of strange sets in terms of cycles","volume":"61","year":"1988","journal-title":"Phys. Rev. Lett."},{"key":"2023080922073594300_c9","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1088\/0951-7715\/3\/2\/006","article-title":"Recycling of strange sets: II. Applications","volume":"3","year":"1990","journal-title":"Nonlinearity"},{"key":"2023080922073594300_c10","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1103\/PhysRevLett.58.112","article-title":"Transition to turbulence via spatio-temporal intermittency","volume":"58","year":"1987","journal-title":"Phys. Rev. Lett."},{"key":"2023080922073594300_c11","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1088\/0951-7715\/7\/1\/007","article-title":"Spatiotemporal intermittency regimes of the one-dimensional complex Ginzburg-Landau equation","volume":"7","year":"1994","journal-title":"Nonlinearity"},{"key":"2023080922073594300_c12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0375-9601(79)90255-X","article-title":"Intermittency and the Lorenz model","volume":"75","year":"1979","journal-title":"Phys. Lett. A"},{"key":"2023080922073594300_c13","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/BF01197757","article-title":"Intermittent transition to turbulence in dissipative dynamical systems","volume":"74","year":"1980","journal-title":"Commun. Math. Phys."},{"key":"2023080922073594300_c14","volume-title":"An Introduction to Chaotic Dynamical Systems","year":"1989"},{"key":"2023080922073594300_c15","doi-asserted-by":"publisher","first-page":"2928","DOI":"10.1103\/PhysRevLett.75.2928","article-title":"Semiclassical quantization of intermittency in helium","volume":"75","year":"1995","journal-title":"Phys. Rev. Lett."},{"key":"2023080922073594300_c16","doi-asserted-by":"publisher","first-page":"1641","DOI":"10.1088\/0951-7715\/9\/6\/015","article-title":"The semiclassical resonance spectrum of hydrogen in a constant magnetic field","volume":"9","year":"1996","journal-title":"Nonlinearity"},{"key":"2023080922073594300_c17","doi-asserted-by":"publisher","first-page":"2863","DOI":"10.1088\/0305-4470\/30\/8\/028","article-title":"How chaotic is the stadium billiard? A semiclassical analysis","volume":"30","year":"1997","journal-title":"J. Phys. A"},{"key":"2023080922073594300_c18","doi-asserted-by":"publisher","first-page":"4201","DOI":"10.1103\/PhysRevLett.78.4201","article-title":"Stability ordering of cycle expansions","volume":"78","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"2023080922073594300_c19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1143\/PTPS.150.1","article-title":"Cycle expansions for intermittent maps","volume":"150","year":"2003","journal-title":"Prog. Theor. Phys. Supp."},{"key":"2023080922073594300_c20","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1088\/0305-4470\/27\/3\/020","article-title":"Determination of resonance spectra for bound chaotic systems","volume":"27","year":"1994","journal-title":"J. Phys. A"},{"key":"2023080922073594300_c21","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1007\/BF02101844","article-title":"Induced maps, Markov extensions and invariant measures in one-dimensional dynamics","volume":"168","year":"1995","journal-title":"Commun. Math. Phys."},{"key":"2023080922073594300_c22","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1017\/S0143385700007963","article-title":"Topological conditions for the existence of invariant measures for unimodal maps","volume":"14","year":"1994","journal-title":"Ergod. Theor. Dyn. Syst."},{"key":"2023080922073594300_c23","doi-asserted-by":"publisher","first-page":"71","DOI":"10.2307\/1971501","article-title":"Distortion of s-unimodal maps","volume":"132","year":"1990","journal-title":"Ann. Math."},{"key":"2023080922073594300_c24","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1007\/BF02102040","article-title":"Markov partition in non-hyperbolic interval dynamics","volume":"138","year":"1991","journal-title":"Commun. Math. Phys."},{"key":"2023080922073594300_c25","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1007\/BF01060077","article-title":"Maps of intervals with indifferent fixed points: Thermodynamic formalism and phase transitions","volume":"66","year":"1992","journal-title":"J. Stat. Phys."},{"issue":"2","key":"2023080922073594300_c26","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1214\/13-aihp586","article-title":"Weak convergence to stable L\u00e9vy processes for nonuniformly hyperbolic dynamical systems","volume":"51","year":"2015","journal-title":"Annal. Inst. H. Poincar\u00e9 Probab. Statist."},{"key":"2023080922073594300_c27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01941319","article-title":"Invariant measures for Markov maps of the interval","volume":"69","year":"1979","journal-title":"Commun. Math. Phys."},{"key":"2023080922073594300_c28","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/BF01941800","article-title":"Absolutely continuous invariant measures for one-parameter families of one-dimensional maps","volume":"81","year":"1981","journal-title":"Commun. Math. Phys."},{"key":"2023080922073594300_c29","doi-asserted-by":"publisher","volume-title":"The Ruelle-Araki Transfer Operator in Classical Statistical Mechanics","year":"1980","DOI":"10.1007\/BFb0017919"},{"key":"2023080922073594300_c30","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1088\/0951-7715\/8\/1\/002","article-title":"Approximate zeta functions for the Sinai billiard and related systems","volume":"8","year":"1995","journal-title":"Nonlinearity"},{"key":"2023080922073594300_c31","doi-asserted-by":"publisher","first-page":"1237","DOI":"10.1088\/0951-7715\/5\/6\/003","article-title":"The correlation spectrum for hyperbolic analytic maps","volume":"5","year":"1992","journal-title":"Nonlinearity"},{"key":"2023080922073594300_c32","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1016\/0167-2789(91)90227-Z","article-title":"Periodic orbits as the skeleton of classical and quantum chaos","volume":"51","year":"1991","journal-title":"Physica D"},{"key":"2023080922073594300_c33","volume-title":"Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics","year":"2004"},{"key":"2023080922073594300_c34","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1007\/BF01076126","article-title":"Construction of Markov partitions","volume":"2","year":"1968","journal-title":"Funct. Anal. Appl.+"},{"key":"2023080922073594300_c35","volume-title":"Symbolic Dynamics: One-Sided, Two-Sided and Countable State Markov Shifts","year":"2012"},{"key":"2023080922073594300_c36","volume-title":"Iterated Maps on the Interval as Dynamical Systems","year":"2009"},{"key":"2023080922073594300_c37","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/0097-3165(73)90033-2","article-title":"On finite limit sets for transformations on the unit interval","volume":"15","year":"1973","journal-title":"J. Comb. Theory A"},{"issue":"7","key":"2023080922073594300_c38","doi-asserted-by":"publisher","first-page":"1114","DOI":"10.1080\/09500348814551201","article-title":"Deterministic chaos: An introduction","volume":"35","year":"1988","journal-title":"J. Mod. Opt."},{"key":"2023080922073594300_c39","doi-asserted-by":"publisher","first-page":"016217","DOI":"10.1103\/PhysRevE.69.016217","article-title":"Variational method for finding periodic orbits in a general flow","volume":"69","year":"2004","journal-title":"Phys. Rev. E"},{"key":"2023080922073594300_c40","volume-title":"New Methods for the Determination of Orbits of Comets","year":"1805"}],"container-title":["Chaos: An Interdisciplinary Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/5.0087463\/16498396\/083115_1_online.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/5.0087463\/16498396\/083115_1_online.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,9]],"date-time":"2023-08-09T22:07:50Z","timestamp":1691618870000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/cha\/article\/32\/8\/083115\/2835963\/Wielding-intermittency-with-cycle-expansions"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,1]]},"references-count":40,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2022,8,1]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0087463","relation":{},"ISSN":["1054-1500","1089-7682"],"issn-type":[{"value":"1054-1500","type":"print"},{"value":"1089-7682","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2022,8]]},"published":{"date-parts":[[2022,8,1]]},"article-number":"083115"}}