This paper analyzes economic uctuations in an overlapping generations economy with productive capital in which random shocks in aggregate productivity are present. Under speci c assumptions we obtain an explicit solution of the model. Applying random dynamical systems theory, we can prove that the long-run behavior of the economy is uniquely described by an asymptotically stable random xed poin...

This review is devoted to dynamical systems in fields of p-adic numbers: origin of p-adic dynamics in p-adic theoretical physics (string theory, quantum mechanics and field theory, spin glasses), continuous dynamical systems and discrete dynamical systems. The main attention is paid to discrete dynamical systems iterations of maps in the field of p-adic numbers (or their algebraic extensions): ...

By counting the numbers of periodic points of all periods for some interval maps, we obtain infinitely many new congruence identities in number theory. Let S be a nonempty set and let f be a map from S into itself. For every positive integer n, we define the n iterate of f by letting f 1 = f and f = f ◦ f for n ≥ 2. For y ∈ S, we call the set { f(y) : k ≥ 0 } the orbit of y under f . If f(y) = ...

This chapter introduces some key concepts that underlie the framework and methodology for modeling and simulation (M&S) originally presented in “Theory of Modeling and Simulation” published in 1976 − referred to hereafter as TMS76 to distinguish it from the current revised edition TMS98. Perhaps the most basic concept is that of mathematical systems theory. First developed in the nineteen sixti...

Gibson developed the affordance concept to complement his theory of direct perception that stands in sharp contrast with the prevalent inferential theories of perception. A comparison of the two approaches shows that the distinction between them also has an ontological aspect. We trace the history and newer formalizations of the notion of affordance and discuss some competing opinions on its sc...

in this paper, we introduce the concept of dynamical distance on a nuclear con-guration space. we partition the nuclear conguration space into disjoint classes. this clas-sication coincides with the classical partitioning of molecular systems via the concept ofconjugacy of dynamical systems. it gives a quantitative criterion to distinguish dierentmolecular structures.