Keller G, Otani A (2017)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2017
Book Volume: 18
Journal Issue: 2
DOI: 10.1142/S0219493718500090
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(𝜃,y)=(T𝜃,f𝜃(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">f𝜃 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.
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).
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