A centralizing monoid M is a set of unary operations which commute with some F operations. Here, called witness . On 3-element set, maximal if and only it has constant operation or majority minimal as its witness. In this paper, we take one such operation, corresponds to monoid, on obtain generalization, mb , k-element for any k >= 3. We explicitly describe the M(mb ) then prove that not &gt...

In this thesis, we establish extreme value (EV) theory and dynamical BorelCantelli lemmas for a class of deterministic chaotic dynamical systems. We establish the distributional convergence (to the three classical extreme value distributions) of the scaled sequence of partial maxima of some time series arising from an observable on systems such as the planar dispersing billiards, Lozi-like maps...

We examine iteration of certain skew-products on the bidisk whose components are rational inner functions, with emphasis simple maps form $\Phi (z_1,z_2) = (\phi (z_1,z_2), z_2)$. If $\phi $ has degree $1$ in first variable, dynamics

Anzai skew-products are shown to be uniquely ergodic with respect the fixed-point subalgebra if and only there is a unique conditional expectation onto such which invariant under dynamics. For particular case of skew-products, this solves question raised by B. Abadie K. Dykema in wider context $$C^*$$ -dynamical systems.

In this paper, we introduce three notions of topological entropy a free semigroup action generated by proper maps for noncompact subsets, which extends the defined Ju et al. [13] and Ma [17]. By using one-point compactification as bridge, study relations entropies between two dynamical systems. We then skew-product transformations, particular subset, relationship upper capacity maps, transforma...

The Kahan discretization of the Lotka-Volterra system, associated with any skew-symmetric graph Γ, leads to a family rational maps, parametrized by step size. When these maps are Poisson respect quadratic structure we say that Γ has Kahan-Poisson property. We show if is connected, it property and only cloning vertices $1,2,\dots ,n$ , an arc i → j precisely when < j, all arcs having same value....