STATISTICAL STABILITY FOR BARGE-MARTIN ATTRACTORS DERIVED FROM TENT MAPS

Autor(es)

Boyland, Philip ^[1] ; de Carvalho, Andre ^[2] ; Hall, Toby ^[3]

Afiliação do(s) autor(es)

^[1] Univ Florida, Dept Math, 372 Little Hall, Gainesville, FL 32611 - USA

^[2] IME USP, Dept Matemat Aplicada, Rua Do Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

^[3] Univ Liverpool, Dept Math Sci, Liverpool L69 7ZL, Merseyside - England

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 40, n. 5, p. 2903-2915, MAY 2020.
• Citações Web of Science: 0

Resumo

Let [f(t)](t is an element of(1,2]) be the family of core tent maps of slopes t. The parameterized Barge-Martin construction yields a family of disk homeomorphisms Phi(t): D-2 -> D-2, having transitive global attractors Lambda(t) on which Phi(t) is topologically conjugate to the natural extension of f(t). The unique family of absolutely continuous invariant measures for f t induces a family of ergodic Phi(t)-invariant measures nu(t), supported on the attractors Lambda(t). We show that this family nu(t), varies weakly continuously, and that the measures nu(t) are physical with respect to a weakly continuously varying family of background Oxtoby-Ulam measures rho(t). Similar results are obtained for the family chi(t): S-2 -> S-2 of transitive sphere homeomorphisms, constructed in a previous paper of the authors as factors of the natural extensions of f(t). (AU)

• Processo FAPESP: 16/25053-8 - Dinâmica e geometria em baixas dimensões
• Beneficiário: André Salles de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Temático