Abstract We consider skew tent maps Tα, β(x) such that (α,β)∈[0,1]2 is the turning point of TTα, β, that is, Tα, β = βα $\begin{array}{} \frac{{\beta}}{{\alpha}} \end{array} $x for 0≤ x ≤ α and Tα,… Expand

Abstract We give examples of non-integrable measurable functions for which there are ‘many’ rotations such that the arithmetic (ergodic) averages exist for almost every x. We also show that if the… Expand

Suppose that f: ℝ → ℝ is a given measurable function, periodic by 1. For an α ∈ ℝ put Mnαf(x) = 1/n+1 Σk=0nf(x + kα). Let Γf denote the set of those α’s in (0;1) for which Mnαf(x) converges for… Expand

An interval map is said to have an asymptotic measure if the time averages of the iterates of Lebesgue measure converge weakly. We construct quadratic maps which have no asymptotic measure. We also… Expand

The statistical properties of the Lyapunov exponent of the chaotic generalized skew tent map is studied. Expressions of the mean and the variance of this Lyapunov exponent at each discrete time index… Expand

AbstractThe rotation set, Γ, of a Lebesgue measurable real valued function on the circle is the set of α ε R for which
$$\tfrac{1}{{n + 1}}\sum _{k = 0}^n f(x + k\alpha )$$
converges as n → ∞ for… Expand

Motivation and Interpretation.- One-Parameter Families of Maps.- Typical Behavior for One Map.- Parameter Dependence.- Systematics of the Stable Periods.- On the Relative Frequency of Periodic and… Expand