74 citations · 195 across the 43 of their papers we have counts for
23 papers · 1 filter
Almost Periodicity in Exponential Dichotomous Linear Dynamics with Piecewise Constant Argument
Marat Akhmet, Furkan Duraner
The paper examines an inhomogeneous system of differential equations with generalized piecewise constant arguments. The focus of the research is on the almost periodicity of both t…
Modulo periodic Poisson stable solutions of quasilinear differential equations
Marat Akhmet, Madina Tleubergenova, Akylbek Zhamanshin
We introduce a new type of recurrence in the space of continuous and bounded functions. The property is easily verifiable, and can be considered for differential equations. This ti…
Deterministic chaos for Markov chains
Marat Akhmet
We find that Markov chains with finite state space are Poincare chaotic. Moreover, finite realizations of the chains are arcs of each unpredictable orbit for sure. An illustrating…
Abstract hyperbolic chaos
Marat Akhmet
The abstract hyperbolic sets are introduced. Continuous and differentiable mappings as well as rate of convergence and transversal manifolds are not under discussion, and the symbo…
Unpredictable Strings
Marat Akhmet, Astrit Tola
A novel notion of unpredictable strings is revealed and utilized to define deterministic unpredictable sequences on a finite number of symbols. We prove the first law of large stri…
Modular chaos for random processes
Marat Akhmet
In the present paper, an essential generalization of the symbolic dynamics is considered. We apply the notions of abstract self-similar sets and the similarity map for a chaos intr…