Recurrence, Dimensions, and Lyapunov Exponents

Keywords

Mathematics, Lyapunov exponent, Mathematical physics, Physics, Mathematical analysis

References

• On the algorithmic complexity of the trajectories of points in dynamical systemsHomer White, Karl Petersen — 1991
• Entropy and data compressionE. H. Farr, A. J. Sarantakis, N. S. Tzannes — 1970
• The Hausdorff Dimension of an Ergodic Invariant Measure for a Piecewise Monotonic Map of the IntervalFranz Hofbauer, Peter Raith — 1992
• Introduction to the Modern Theory of Dynamical SystemsJ.A. Zukas — 1998
• Multifractal properties of return time statistics.Nicolai Hadyn, José Luevano, Giorgio Mantica — 2001
• Pointwise dimensions for Poincaré recurrences associated with maps and special flowsValentin Afraimovich, Jean-René Chazottes, Benoît Saussol — 2002
• Entropy and the complexity of the trajectories of a dynamical systemA A Brudno — 1978
• Pesin's dimension for Poincare recurrences.Valentin Afraimovich — 1997
• Hausdorff Dimension of Measures¶via Poincaré RecurrenceLuís Barreira, Benoît Saussol — 2001
• AN ENTROPY ESTIMATOR FOR A CLASS OF INFINITE ALPHABET PROCESSESAnthony Quas — 1999
• Nonparametric Entropy Estimation for Stationary Processesand Random Fields, with Applications to English TextIoannis Kontoyiannis, P. Algoet, Yu. M. Suhov — 1998
• Dimensions for recurrence times: topological and dynamical propertiesVincent Penné, Benoît Saussol, Sandro Vaienti — 1999
• Statistics of Return Times:¶A General Framework and New ApplicationsM. Hirata, Benoît Saussol, Sandro Vaienti — 1999
• Algorithmic complexity of points in dynamical systemsHomer White — 1993
• Product structure of Poincaré recurrenceLuís Barreira, Benoît Saussol — 2002
• Local dimension for piecewise monotonic maps on the intervalFranz Hofbauer — 1995
• Introduction to the modern theory of dynamical systemsKatok, Anatole, Hasselblatt, Boris — 1996
• An inequality for the Ljapunov exponent of an ergodic invariant measure for a piecewise monotonic map of the intervalF. Hofbauer — 1991

Cited by

• The recurrence dimension for piecewise monotonic maps of the intervalFranz Hofbauer — 2005
• How much information about a dynamical system do its recurrences containGeoffrey R. Robinson, Marco Thiel — 2007
• Local return rates in Sturmian subshiftsMichal Kupsa — 2011
• The spectrum of Poincaré recurrenceKa‐Sing Lau, Lin Shu — 2008
• Statistics of return times and Hausdorff dimensionŁ. Pawelec — 2014
• Local and global approaches to the problem of Poincaré recurrences. Applications in nonlinear dynamicsВ. С. Анищенко, Ya. I. Boev, Nadezhda Semenova — 2015
• Теорема Семереди и задачи об арифметических прогрессиях@@@Szemerédi's theorem and problems on arithmetic progressionsИлья Дмитриевич Шкредов, Il'ya Dmitrievich Shkredov — 2006
• The recurrence time for irrational rotationsDong Han Kim — 2006
• Hitting time and dimension in Axiom A systems and generic interval excangesStefano Galatolo — 2005
• Quantitative recurrence properties of expanding mapsJosé Fernández, María V. Melián, Domingo Pestana — 2007
• The distribution of the overlapping functionMiguel Abadi, Rodrigo Lambert — 2011
• Chaotic Generator in Digital Secure CommunicationShu-Ming Chang — 2009
• Primeiro tempo de retorno para processos β-mixingErika Alejandra Rada Mora — 2014
• On the Statistical Distribution of First-Return Times of Balls and Cylinders in Chaotic SystemsG. MANTICA, S. VAIENTI — 2009
• Entropy and Poincaré recurrence from a geometrical viewpointPaulo Varandas — 2008
• On the hitting depth in the dynamical system of continued fractionsPeng Li — 2014
• Recurrence networks—a novel paradigm for nonlinear time series analysisReik V. Donner, Yong Zou, Jonathan F. Donges — 2009
• Speed of convergence for laws of rare events and escape ratesAna Cristina Moreira Freitas, Jorge Milhazes Freitas, Mike Todd — 2014
• Dimension via Waiting time and RecurrenceStefano Galatolo — 2003
• The waiting time for irrational rotationsDong Han Kim, Byoung Ki Seo — 2003

Related papers

• ИСПОЛЬЗОВAНИЕ ПОТЕНЦИAЛA СОЦИAЛЬНЫХ ПAРТНЕРОВ В ПОДГОТОВКЕ БУДУЩИХ ПЕДAГОГОВБ.Б. Атaбекова — 2024
• The instantaneous Lyapunov exponent and its application to chaotic dynamical systemsKihong Shin, J.K. Hammond — 1998
• Primärzerlegung in Steinschen AlgebrenOtto Förster — 1964
• Application of Lyapunov Exponents to Fault Diagnosis of Rolling BearingYang Shaopu — 2007
• The matric algorithm of Lyapunov exponent for the experimental data obtained in dynamic analysisJunhai Ma, Chen Yushu, Liu Zengrong — 1999
• Über unirationale Scharen auf algebraischen MannigfaltigkeitenLudwig Reich — 1966
• Study of fault diagnosis of rolling bearings based on the largest Lyapunov exponentShang-Xin Zhao, Laibin Zhang, Zhaohui Wang — 2005
• A practical method to compute the largest Lyapunov exponentMingchuan Miao, Ruo‐Qian Wang, Shaoqiang Yuan — 2006
• Produkttreue Klassen universeller AlgebrenJürgen Timm — 1969