Chaotically driven sigmoidal maps

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autorinnen und Autoren: Keller G, Otani A
Zeitschrift: Stochastics and Dynamics
Jahr der Veröffentlichung: 2017
Band: 18
Heftnummer: 2
ISSN: 0219-4937
Sprache: Englisch


Abstract

We consider skew product dynamical systems f:Θ×ℝ→Θ×ℝ,f(휃,y)=(T휃,f휃(y))" role="presentation">f:Θ×ℝ→Θ×ℝ,f(��,y)=(T��,f��(y)) with a (generalized) baker transformation T" role="presentation">T at the base and uniformly bounded increasing C3" role="presentation">C3 fibre maps f휃" role="presentation">f��
with negative Schwarzian derivative. Under a partial hyperbolicity
assumption that ensures the existence of strong stable fibres for f" role="presentation">f,
we prove that the presence of these fibres restricts considerably the
possible structures of invariant measures — both topologically and
measure theoretically, and that this finally allows to provide a
“thermodynamic formula” for the Hausdorff dimension of set of those base
points over which the dynamics are synchronized, i.e. over which the
global attractor consists of just one point.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Keller, Gerhard Prof. Dr.
Professur für Mathematik (Ergodentheorie)
Otani, Atsuya
Professur für Mathematik (Ergodentheorie)


Zitierweisen

APA:
Keller, G., & Otani, A. (2017). Chaotically driven sigmoidal maps. Stochastics and Dynamics, 18(2). https://dx.doi.org/10.1142/S0219493718500090

MLA:
Keller, Gerhard, and Atsuya Otani. "Chaotically driven sigmoidal maps." Stochastics and Dynamics 18.2 (2017).

BibTeX: 

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