The statistical properties of endomorphisms under the assumption that the associated Perron– Frobenius operator is quasicompact are considered. In particular, the central limit theorem, weak invariance principle and law of the iterated logarithm for sufficiently regular observations are examined. The approach clarifies the role of the usual assumptions of ergodicity, weak mixing, and exactness....

Let (Mn) be a sequence of positive numbers satisfying M0 = 1 and Mn+m MnMm ≥ ( n+m n ) , m, n, non-negative integers. We let D([0, 1],M) = {f ∈ C∞([0, 1]) : ‖f‖ = ∞ ∑

In this paper, the endomorphisms, the half-strong endomorphisms, the locally strong endomorphisms, the quasi-strong endomorphisms, the strong endomorphisms and the automorphisms of a join of cycle n C and a vertex y are investigated. Some enumerative problems concerning these graphs are solved. In particular, the endomorphism spectrums and the endomorphism types of these graphs are given. It ha...

We investigate the interrelationships between the dynamical properties of commuting continuous maps of a compact metric space. Let X be a compact metric space. First we show the following. If τ : X → X is an expansive onto continuous map with the pseudo-orbit tracing property (POTP) and if there is a topologically mixing continuous map φ : X → X with τφ = φτ , then τ is topologically mixing. If...