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SUMMARY:Singularity of Lévy walks in the lifted Pomeau-Manneville map - S
 amuel Brevitt (Queen Mary University of London)
DTSTART:20240904T110500Z
DTEND:20240904T112500Z
UID:TALK219130@talks.cam.ac.uk
DESCRIPTION:It is well-known that simple deterministic dynamical systems c
 an display intermittent dynamics leading to anomalous diffusion. An exampl
 e is the Pomeau-Manneville (PM) map which\, suitably lifted onto the whole
  real line\, generates superdiffusion that can be reproduced by stochastic
  L&eacute\;vy walks (LWs). Here we report that this matching only holds fo
 r parameter values of the PM map that are of Lebesgue measure zero in its 
 two-dimensional parameter space. This is due to a bifurcation scenario tha
 t the map exhibits under variation of one parameter. Constraining this par
 ameter to specific singular values at which the map generates superdiffusi
 on\, and varying the second parameter\, we find quantitative deviations be
 tween deterministic PM diffusion and stochastic LW diffusion in a particul
 ar range of parameter values\, which cannot be cured by simple LW modifcat
 ions. We also explore the effect of aging on superdiffusion in the PM map 
 and show that this yields a profound change of the diffusive properties un
 der variation of the aging time\, which should be important for experiment
 s.\nAuthors: S. Brevitt\, A. Schulz\, D. Pegler\, H. Kantz\, R. Klages
LOCATION:Seminar Room 1\, Newton Institute
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