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Let f be a nonrenormalizable S-unimodal map. We prove that f is a Collet-Eckmann map if its dynamical zeta function looks like that of a uniformly hyperbolic map.
For a class of quasiperiodically forced time-discrete dynamical systems of two variables (θ,x) ∈ with nonpositive Lyapunov exponents we prove the existence of an attractor Γ̅ with the following properties:
1. Γ̅ is the closure of the graph of a function x = ϕ(θ). It attracts Lebesgue-a.e. starting point in . The set θ:ϕ(θ) ≠ 0 is meager but has full 1-dimensional Lebesgue measure.
2. The omega-limit of Lebesgue-a.e point in is , but for a residual set of points in the omega limit is the...
We combine some results from the literature to give examples of completely mixing interval maps without limit measure.
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