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Random walks generated by area preserving maps with zero Lyapounov exponents

Authors :
Maurice Courbage
M. Bernardo
T. T. Truong
Source :
Communications in Nonlinear Science and Numerical Simulation. 8:189-199
Publication Year :
2003
Publisher :
Elsevier BV, 2003.

Abstract

WestudytheasymptoticlimitdistributionsofBirkhoffsumsS n ofasequenceofrandomvariablesofdynamicalsystemswithzeroentropyandLebesguespectrumtype.Adynamicalsystemofthisfamilyisaskewproductoveratranslationbyananglea.Thesequencehaslongmemoryeffects.Itcomesthatwhena=p isirrationaltheasymptoticbehaviorofthemomentsofthenormalizedsumsS n =f n dependsonthepropertiesofthecontinuousfractionexpansionofa.Inparticular,themomentsoforderk,EððS n =ffiffiffinpÞ k Þ,arefiniteandboundedwithrespectton whena=p hasboundedcontinuousfractionexpansion.Theconsequencesofthesepropertiesonthevalidityornotofthecentrallimittheoremarediscussed. 2003ElsevierB.V.Allrightsreserved. PACS:05.40;05.45Keywords:Weakchaos;Centrallimittheorem;Diffusioncoefficients 1. IntroductionKinetictheoryofgaseshaspermittedtoderivetransportprocesses,liketheBrownianmotion,fromtheLiouvilleequation.Manyworkshavebeendevotedtoderivediffusionprocessesfromchaoticdeterministicdynamicalsystems.OneofthepioneeringworkshasbeendonebySina€iifortheLorentzgasintwodimensionswhichisasystemofnon-interactingparticlesmovingwithconstantvelocityandbeingelasticallyreflectedfromperiodicallydistributedscattererswith

Details

ISSN :
10075704
Volume :
8
Database :
OpenAIRE
Journal :
Communications in Nonlinear Science and Numerical Simulation
Accession number :
edsair.doi...........0de3a8646639f699ae6c7f65403c3acd