Modular Chaos for Random Processes

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 introduction, which orbits are expanded among infinitely many modules. The dynamics is free of dimensional, metrical and topological assumptions. It unites all the three types of Poincar´e, Li-Yorke and Devaney chaos in a single model, which can be unbounded. The research demonstrates that the dynamics of Poincar´e chaos is of exceptional use to analyze discrete and continuous-time random processes. Examples, illustrating the results are provided.
Discontinuity, Nonlinearity, and Complexity


Hierarchical control with partial observations: Sufficient conditions
Boutin, Olivier; Komenda, Jan; Masopust, Tomas; Schmidt, Klaus Verner; Van Schuppen, Jan H. (2011-12-01)
In this paper, hierarchical control of both monolithic and modular discrete-event systems under partial observations is studied. Two new conditions, called observation consistency and local observation consistency, are proposed. These conditions are sufficient for the preservation of observability between the original and the abstracted plant. Moreover, it is shown that both conditions are compositional, that is, they are preserved by the synchronous product. This property makes it possible to use hierarchi...
ATALAY, MERT; PARKAN, BARIŞ; Department of Philosophy (2022-9)
This thesis develops an account of value pluralism which claims that the conception of “the political” is constituted by value pluralism and accordingly, “the political” is the sphere that is comprised of plural values and aims. Within this account of value pluralism, making compromises is accepted to be the viable option of resolving conflicts and disagreements in the political sphere. Besides, as this thesis argues, when compromises are made sensibly, the plural ways of expression are maintained in the po...
Optimal control of stochastic hybrid system with jumps: A numerical approximation
Temoçin, Büşra Zeynep; Weber, Gerhard Wilhelm (2014-03-15)
The generalized class of stochastic hybrid systems consists of models with regime changes including the occurrence of impulsive behavior. In this paper, the stochastic hybrid processes with jumps are approximated by locally consistent Markov decision processes that preserve local mean and covariance. We further apply a randomized switching policy for approximating the dynamics on the switching boundaries. To investigate the validity of the approximation, we study a stochastic optimal control problem. On the...
Abstract Hyperbolic Chaos
Akhmet, Marat (2022-01-01)
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 symbolic dynamics paradigm is realized in a new way. Our suggestions are for more neat comprehension of chaos in the domain. The novelties can serve for revisited models as well as motivate new ones.
Isomorphism classes of elliptic curves over finite fields of characteristic two
Kırlar, Barış Bülent; Akyıldız, Ersan; Department of Mathematics (2005)
In this thesis, the work of Menezes on the isomorphism classes of elliptic curves over finite fields of characteristic two is studied. Basic definitions and some facts of the elliptic curves required in this context are reviewed and group structure of elliptic curves are constructed. A fairly detailed investigation is made for the isomorphism classes of elliptic curves due to Menezes and Schoof. This work plays an important role in Elliptic Curve Digital Signature Algorithm. In this context, those isomorphi...
Citation Formats
M. Akhmet, “Modular Chaos for Random Processes,” Discontinuity, Nonlinearity, and Complexity, vol. 11, no. 2, pp. 191–201, 2022, Accessed: 00, 2022. [Online]. Available: