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Abstract

We begin by studying the non-autonomous ordinary differential equation
$$ \dot x = f\left( {t,x} \right) $$
where U ⊂ R×Rd is open, and (t, x) ∈ U, and f: U → Rd is continuous. For a curve φ we let Dφ denote its domain, which is an interval. By a solution φ we always will mean a “non-continuable” solution; i.e., there is no solution Ψ (defined on any interval DΨ) such that DΩ ⊂ DΩ, DΩ ≠ Dφ, and Ω ≡ φ on Dφ. We are also interested in studying other systems with non-uniqueness including the contingent equation \( \dot x \in \Omega \left( {t,x} \right), \) , and the control equation \( \dot x = g\left( {t,x,u} \right) \) for u ∈ Λ, where various additional conditions may be put on the integrable function u(•) or on the set g(t, x, Λ). In general we are interested in the set S of curves or solutions (with varying domains) which represent some kind of non-autonomous dynamical system without uniqueness.

Keywords

Curve Space Contingent Equation Rest Point Mathematical System Theory Autonomous Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1969

Authors and Affiliations

  • James A. Yorke

There are no affiliations available

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