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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

CRITICAL COVERING MAPS WITHOUT ABSOLUTELY CONTINUOUS INVARIANT PROBABILITY MEASURE

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Author(s):
Lloyd, Simon [1] ; Vargas, Edson [2]
Total Authors: 2
Affiliation:
[1] Xian Jiaotong Liverpool Univ, Dept Math Sci, 111 Renai Rd, Suzhou 215123 - Peoples R China
[2] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo - Brazil
Total Affiliations: 2
Document type: Journal article
Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 39, n. 5, p. 2393-2412, MAY 2019.
Web of Science Citations: 0
Abstract

We consider the dynamics of smooth covering maps of the circle with a single critical point of order greater than 1. By directly specifying the combinatorics of the critical orbit, we show that for an uncountable number of combinatorial equivalence classes of such maps, there is no periodic attractor nor an ergodic absolutely continuous invariant probability measure. (AU)

FAPESP's process: 17/10106-1 - Ergodicity and asymmetry in one dimensional dynamics
Grantee:Edson Vargas
Support Opportunities: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 11/01482-3 - Dynamics with critical points of mixed criticality
Grantee:Simon Trevor Lloyd
Support Opportunities: Scholarships in Brazil - Post-Doctoral