Classical and new results concerning the topological structure of skew-products semiflows, coming from non-autonomous maps and differential equations, are combined in order to establish rigorous conditions giving rise to the occurrence of strange nonchaotic attractors. A special attention is paid to the relation of these sets with the almost automorphic extensions of the base flow. The scope of...

We investigate algebraic Zd-actions of entropy rank one, namely those for which each element has finite entropy. Such actions can be completely described in terms of diagonal actions on products of local fields using standard adelic machinery. This leads to numerous alternative characterizations of entropy rank one, both geometric and algebraic. We then compute the measure entropy of a class of...

We consider the dynamics of semi-hyperbolic semigroups generated by finitely many rational maps on the Riemann sphere. Assuming that the nice open set condition holds it is proved that there exists a geometric measure on the Julia set with exponent h equal to the Hausdorff dimension of the Julia set. Both h-dimensional Hausdorff and packing measures are finite and positive on the Julia set and ...

In this paper, we discuss a generalization of Balakrishnan skew-normal distribution with two parameters that contains the skew-normal, the Balakrishnan skew-normal and the two-parameter generalized skew-normal distributions as special cases. Furthermore, we establish some useful properties and two extensions of this distribution. 

In this paper, we investigate the existence of random absolutely continuous invariant measures (ACIP) for expanding on average Saussol maps in higher dimensions. This is done by establishment a Lasota–Yorke inequality transfer operators space bounded oscillation. We prove that number ergodic skew product ACIPs finite and will provide an upper bound these ACIPs. work can be seen as generalizatio...

Here we build on the result given in [P1] and extend those in [HL2] to functions which are k times differentiable a.e., k > 1. For each k we give, a class of irrational number Sk such that the skew product extension defined by these functions is ergodic for irrational rotations by these numbers. In the second part of this paper we examine the cohomology of functions over the adding machine tran...

where p and q are polynomials. We consider skew products which are Axiom A and extend holomorphically to endomorphisms of P2 of degree d ≥ 2. In the article [DH], we studied orbits of critical points in a distinguished subset of C2, and we constructed new examples of Axiom A maps. We made an erroneous assumption about polynomial skew products, which holds for our main examples but fails in gene...

We evaluate the hyperpfaffian of a skew-symmetric k-ary function polynomial f of degree k/2 · (n−1). The result is a product of the Vandermonde product and a certain expression involving the coefficients of the polynomial f . The proof utilizes a sign reversing involution on a set of weighted, oriented partitions. When restricting to the classical case when k = 2 and the polynomial is (xj − xi)...

We investigate algebraic Z-actions of entropy rank one, namely those for which each element has finite entropy. Such actions can be completely described in terms of diagonal actions on products of local fields using standard adelic machinery. This leads to numerous alternative characterizations of entropy rank one, both geometric and algebraic. We then compute the measure entropy of a class of ...

We study families of hyperbolic skew products with the transversality condition and in particular, the Hausdorff dimension of their fibers, by using thermodynamical formalism. The maps we consider can be non-invertible, and the study of their dynamics is influenced greatly by this fact. We introduce and employ probability measures (constructed from equilibrium measures on the natural extension)...