Keller G, Otani A (2013)
Publication Type: Journal article
Publication year: 2013
Publisher: Taylor & Francis: STM, Behavioural Science and Public Health Titles
Book Volume: 28
Pages Range: 123--139
Journal Issue: 2
DOI: 10.1080/14689367.2013.781267
We study bifurcations of invariant graphs in skew product dynamical systems driven by hyperbolic surface maps T like Anosov surface diffeomorphisms or baker maps and with one-dimensional concave fibre maps under multiplicative forcing when the forcing is scaled by a parameter r=e^{-t}. For a range of parameters two invariant graphs (a trivial and a non-trivial one) coexist, and we use thermodynamic formalism to characterize the parameter dependence of the Hausdorff and packing dimension of the set of points where both graphs coincide. As a corollary we characterize the parameter dependence of the dimension of the global attractor A_t: Hausdorff and packing dimension have a common value dim(A_t), and there is a critical parameter t_c determined by the SRB measure of T^{-1} such that dim(A_t)=3 for t < t_c and t --> dim(A_t) is strictly decreasing for t_c < t < t_{max}.
APA:
Keller, G., & Otani, A. (2013). Bifurcation and Hausdorff dimension in families of chaotically driven maps with multiplicative forcing. Dynamical Systems-An International Journal, 28(2), 123--139. https://doi.org/10.1080/14689367.2013.781267
MLA:
Keller, Gerhard, and Atsuya Otani. "Bifurcation and Hausdorff dimension in families of chaotically driven maps with multiplicative forcing." Dynamical Systems-An International Journal 28.2 (2013): 123--139.
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