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A unified approach to continuous and discrete dynamics. (English) Zbl 0723.34030

Qualitative theory of differential equations, 3rd Colloq., Szeged/Hung. 1988, Colloq. Math. Soc. János Bolyai 53, 37-56 (1990).
[For the entire collection see Zbl 0695.00015.]
The authors define axiomatically a set T and develop the calculus of functions defined on T. The set \({\mathbb{R}}\) of reals and the set \({\mathbb{Z}}\) of integers are particular cases of the set T. If \(T={\mathbb{R}}\), the derivative of a function is the usual derivative and if \(T={\mathbb{Z}}\), the derivative is the difference operator. Therefore the differential equations are generalization both of the ordinary differential equations and of the difference equations. In the paper some properties of solutions of differential equations and some qualitative properties of dynamical systems are studied.

MSC:

37-XX Dynamical systems and ergodic theory
34A99 General theory for ordinary differential equations
39A12 Discrete version of topics in analysis

Citations:

Zbl 0695.00015