BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Pedro Duarte (Univ. Lisbon Portugal) DTSTART:20200417T140000Z DTEND:20200417T150000Z DTSTAMP:20260423T022006Z UID:ResDin/1 DESCRIPTION:Title: H ölder continuity of the Lyapunov exponent for linear cocycles over hyperb olic dynamical systems\nby Pedro Duarte (Univ. Lisbon Portugal) as par t of Resistência dinâmica (Dynamical resistance)\n\n\nAbstract\nTitle: H ölder continuity of the Lyapunov exponent for linear cocycles over hyperb olic dynamical systems\nAbstract: In this talk we explain how to derive Ho lder continuity of the Lyapunov exponent\nfor fiber bunched GL(d\,R)-linea r cocycles over hyperbolic maps. A generic pinching and twisting assumptio n is required. In other words\, if the cocycle is assumed to satisfy the s implicity criterion of Avila and Viana [2] then all Lyapunov exponents dep end Holder continuously on the cocycle matrix valued function.\nTo set the context\, in a recent paper [3]\, Backes\, Brown and Butler proved the co ntinuity of the Lyapunov exponent for fiber bunched GL(2\,R)-linear cocycl es over hyperbolic maps\, without any generic assumption on the cocycle\, thus proving a conjecture of Viana and at the same time generalizing a the orem of Bocker-Neto and Viana [4] about the continuity of the Lyapunov exp onent for locally constant random GL(2\,R)-linear cocycles. The Holder qua ntitative version of [4] (with a generic assumption and for arbitrary dime nsions) was established by E. Le Page many years before in [5]. The corres ponding higher dimensional generalizations of [4] and [3] are respectively a work under preparation [1] by Avila\, Eskin and Viana and something mor e difficult yet to be done.\nJoint work with Silvius Klein e Mauricio Pole tti.\n\n[1] A. Avila\, A. Eskin\, and M. Viana\, Continuity of Lyapunov ex ponents for products random matrices\, In preparation.\n[2] A. Avila and M . Viana\, Simplicity of Lyapunov spectra: a sufficient criterion\, Port. M ath. 64 (2007)\, 311–376.\n[3] L. Backes\, A. Brown\, and C. Butler\, Co ntinuity of Lyapunov exponents for cocycles with invariant holonomies\, Pr eprint http://arxiv.org/pdf/1507.08978v2.pdf.\n[4] C. Bocker-Neto and M. V iana\, Continuity of Lyapunov exponents for random 2d matrices\, preprint (2010)\, 1–38.\n[5] E. Le Page\, Régularité du plus grand exposant car actéristique des produits de matrices aléatoires indépendantes et appli cations\, Annales de l’institut Henri Poincaré (B) Probabilités et Sta tistiques 25 (1989)\, no. 2\, 109–142.\n LOCATION:https://researchseminars.org/talk/ResDin/1/ END:VEVENT END:VCALENDAR