Stability index for chaotically driven concave maps

摘要: We study skew product systems driven by a hyperbolic base map S (e.g. baker or an Anosov surface diffeomorphism) and with simple concave fibre maps on interval [0,a] like h(x)=g(\theta) tanh(x) where g(\theta) is factor the map. The fibre-wise attractor graph of upper semicontinuous function \phi(\theta). For many choices g, \phi has residual set zeros but \phi>0 almost everywhere w.r.t. Sinai-Ruelle-Bowen measure S^(-1). In such situations we evaluate stability index global system, which subgraph \phi, at all regular points (\theta,0) in terms local exponents \Gamma(\theta):=\lim_{n\to\infty} 1/n log g_n(\theta) \Lambda(\theta):=\lim_{n\to\infty} 1/n\log|D_u S^{-n}(\theta)| positive zero s_* certain thermodynamic pressure associated S^(-1) g. (In queuing theory, analogon known as Loyne's exponent.) The was introduced Podvigina Ashwin 2011 to quantify scaling basins attraction.