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Random walks generated by area preserving maps with zero Lyapounov exponents
- 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