Semi-uniform ergodic theorems and applications to forced systems

摘要: In nonlinear dynamics an important distinction exists between uniform bounds on growth rates, as in the definition of hyperbolic sets, and non-uniform theory Liapunov exponents. rare cases, for instance uniquely ergodic systems, it is possible to derive estimates from hypotheses. This allowed one us show a previous paper that strange non-chaotic attractor quasiperiodically forced system could not be graph continuous function. had been conjecture some time. this we generalize convergence time averages systems broader range systems. particular, how conditions rates with respect all invariant measures can used one-sided both Birkhoff sub-additive theorems. We apply latter any compact set must support measure non-negative maximal normal exponent; other words, contain `non-attracting' orbits. was already known few examples attractors have rigorously proved exist. Finally, our semi-uniform theorems arbitrary skew product discuss application such extensions existence attracting graphs.