Brownian motion, random walks on trees, and harmonic measure on polynomial Julia sets

dc.creatorEmerson, Nathaniel D.
dc.date2006-09-04
dc.date2006-09-12
dc.date.accessioned2026-07-07T07:24:26Z
dc.date.available2026-07-07T07:24:26Z
dc.descriptionWe consider the harmonic measure on a disconnected polynomial Julia set in terms of Brownian motion. We show that the harmonic measure of any connected component of such a Julia set is zero. Associated to the polynomial is a combinatorial model, the tree with dynamics. We define a measure on the tree, which is a combinatorial version on harmonic measure. We show that this measure is isomorphic to the harmonic measure on the Julia set. The measure induces a random walk on the tree, which is isomorphic to Brownian motion in the plane.
dc.description15 pages, 5 figures. Revised 9/12/06
dc.identifierhttps://arxiv.org/abs/math/0609044
dc.identifierhttp://arxiv.org/abs/math/0609044
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/116348
dc.subjectDynamical Systems
dc.subject37F10 (Primary); 30C85, 05C8 (Secondary)
dc.titleBrownian motion, random walks on trees, and harmonic measure on polynomial Julia sets
dc.typetext

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