INVARIANT SETS OF STRUCTURALLY STABLE DIFFERENTIAL SYSTEMS

On invariant sets topology

In this paper, we introduce and study a new topology related to a self mapping on a nonempty set.Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets ofX related to f, i.e. f := fA X : f(A) Ag P(X) is a topology on X. Among other things,we nd the smallest open sets contains a point x 2 X. Moreover, we find the relations between fand To f . For insta...

How structurally stable are global socioeconomic systems?

The stability analysis of socioeconomic systems has been centred on answering whether small perturbations when a system is in a given quantitative state will push the system permanently to a different quantitative state. However, typically the quantitative state of socioeconomic systems is subject to constant change. Therefore, a key stability question that has been under-investigated is how st...

Spaceability for Sets of Bandlimited Input Functions and Stable Linear Time-Invariant Systems with Divergence Behavior

The approximation of linear time-invariant systems by sampling series is studied for bandlimited input functions in the Paley-Wiener space PWπ. It has been known that there exist functions and systems such that the approximation process diverges. In this paper we identify a signal set and a system set with divergent Shannon sampling expression. We analyze the structure of these sets and prove t...

Isochronous sets of invariant control systems

Family of Invariant Cantor Sets as orbits of Differential Equations

The invariant Cantor sets of the logistic map gμ(x) = μx(1 − x) for μ > 4 are hyperbolic and form a continuous family. We show that this family can be obtained explicitly through solutions of infinitely coupled differential equations due to the hyperbolicity. The same result also applies to the tent map Ta(x) = a(1/2− |1/2− x|) for a > 2.