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Non-smooth saddle-node bifurcations II: Dimensions of strange attractors

Published online by Cambridge University Press:  04 May 2017

G. FUHRMANN ,
M. GRÖGER  and
T. JÄGER
G. FUHRMANN
Affiliation:
Department of Mathematics, TU Dresden, Germany email Gabriel.Fuhrmann@mailbox.tu-dresden.de, Tobias.Oertel-Jaeger@tu-dresden.de
M. GRÖGER
Affiliation:
Department of Mathematics, Universität Bremen, Germany email groeger@math.uni-bremen.de
T. JÄGER
Affiliation:
Department of Mathematics, TU Dresden, Germany email Gabriel.Fuhrmann@mailbox.tu-dresden.de, Tobias.Oertel-Jaeger@tu-dresden.de
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Abstract

We study the geometric and topological properties of strange non-chaotic attractors created in non-smooth saddle-node bifurcations of quasiperiodically forced interval maps. By interpreting the attractors as limit objects of the iterates of a continuous curve and controlling the geometry of the latter, we determine their Hausdorff and box-counting dimension and show that these take distinct values. Moreover, the same approach allows us to describe the topological structure of the attractors and to prove their minimality.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 8 , December 2018 , pp. 2989 - 3011
Copyright
© Cambridge University Press, 2017 

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