Abstract
The solutions of the autonomous ordinary differential equation $$ \dot{x} = f(x) $$ (1.1) (where ẋ stands for dx/dt) give rise to a semidynamical (even dynamical) system on IRd provided f: W → IRd is continuous on the open subset W ⊂ IRd and the solutions of Equation (1.1) through any point (x0,t0) ∈ W × IR are uniquely defined and remain in W for all time. In fact, if Φ(x0;t) denotes the solution of Equation (1.1) through (x0,0) evaluated at time t ∈ IR+, it can be verified that (W,Φ) is a semidynamical system.
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