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Renormalization for Lorenz maps of monotone combinatorial types
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
2019 (English)In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 39, no 1, p. 132-158Article in journal (Refereed) Published
Abstract [en]

Lorenz maps are maps of the unit interval with one critical point of order rho > 1 and a discontinuity at that point. They appear as return maps of sections of the geometric Lorenz flow. We construct real a priori bounds for renormalizable Lorenz maps with certain monotone combinatorics and a sufficiently flat critical point, and use these bounds to show existence of periodic points of renormalization, as well as existence of Cantor attractors for dynamics of infinitely renormalizable Lorenz maps.

Place, publisher, year, edition, pages
CAMBRIDGE UNIV PRESS , 2019. Vol. 39, no 1, p. 132-158
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Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-372369DOI: 10.1017/etds.2017.12ISI: 000451398100006OAI: oai:DiVA.org:uu-372369DiVA, id: diva2:1276663
Available from: 2019-01-08 Created: 2019-01-08 Last updated: 2019-01-08Bibliographically approved

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Gaidashev, Denis

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