Generating Flows on Metric Spaces
Copyright policy )Generating Flows on Metric Spaces
This paper seeks to obtain solution curves of arc fields and to study the continuous dependence of solutions on initial conditions. The authors present some examples, one of which shows that it is not sufficient to merely assume that the arc field is Lipschitz in order to obtain solution curves. They show that the flow of a certain arc field yields a continuous analog of an iterated function system, where the fixed point of the flow is the convex hull of the fractal fixed point of the discrete version of the system.
- University of Hawaii System United States
- University of Hawaiʻi Sea Grant United States
- Metropolitan State University United States
solution curves of arc fields, Applied Mathematics, metric space, Cauchy–Lipschitz Theorem, Nonlinear differential equations in abstract spaces, iterated function system, fractal fixed point, Continuity properties of mappings on manifolds, continuous dependence of solutions on initial conditions, flow, Dynamics induced by flows and semiflows, Analysis
solution curves of arc fields, Applied Mathematics, metric space, Cauchy–Lipschitz Theorem, Nonlinear differential equations in abstract spaces, iterated function system, fractal fixed point, Continuity properties of mappings on manifolds, continuous dependence of solutions on initial conditions, flow, Dynamics induced by flows and semiflows, Analysis
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