• Corpus ID: 231830516

Isentropes, Lyapunov exponents and Ergodic averages

  title={Isentropes, Lyapunov exponents and Ergodic averages},
  author={Gabriella Keszthelyi and Zolt'an Buczolich},

Figures from this paper


Equi-topological entropy curves for skew tent maps in the square
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,
Chaos on the Interval
Kneading sequences of skew tent maps
Arithmetic averages of rotations of measurable functions
  • Z. Buczolich
  • Mathematics
    Ergodic Theory and Dynamical Systems
  • 1996
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
Non-L1 functions with rotation sets of Hausdorff dimension one
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
Quadratic maps without asymptotic measure
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
On statistical properties of the lyapunov exponent of the generalized skew tent map
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
A Function with Locally Uncountable Rotation Set
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
Iterated maps on the interval as dynamical systems
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