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SUMMARY:Maxime Breden & Maximilian Engel (École Polytechnique\, France & 
 Freie Universität Berlin\, Germany)
DTSTART:20200825T140000Z
DTEND:20200825T150000Z
DTSTAMP:20260423T024621Z
UID:CRM-CAMP/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CRM-CAMP/9/"
 >Computer-assisted proof of shear-induced chaos in stochastically perturbe
 d Hopf systems</a>\nby Maxime Breden & Maximilian Engel (École Polytechni
 que\, France & Freie Universität Berlin\, Germany) as part of CRM CAMP (C
 omputer-Assisted Mathematical Proofs) in Nonlinear Analysis\n\n\nAbstract\
 nIn this talk\, we discuss a long-standing conjecture concerning shear-ind
 uced chaos in stochastically perturbed systems exhibiting a Hopf bifurcati
 on. Using the recently developed theory of conditioned Lyapunov exponents 
 on bounded domains\, we reformulate the problem into the rigorous computat
 ion of eigenvectors of some elliptic PDEs\, namely the Kolmogorov/Fokker-P
 lanck equations describing distributions of the underlying stochastic proc
 ess\, and are thus able to prove that  the first Lyapunov exponent is posi
 tive for certain parameter regimes.\n
LOCATION:https://researchseminars.org/talk/CRM-CAMP/9/
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