| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [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
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 40, n. 5, p. 2903-2915, MAY 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 16/25053-8 - Dynamics and geometry in low dimensions |
| Grantee: | André Salles de Carvalho |
| Support Opportunities: | Research Projects - Thematic Grants |