# Article

Full entry | PDF   (0.8 MB)
Keywords:
periodic system; period map; invariant set; flow
Summary:
We investigate the nonautonomous periodic system of ODE’s of the form $\dot{x}=\vec{v}(x)+r_{p}(t)(\vec{w}(x)-\vec{v}(x))$, where $r_{p}(t)$ is a $2p$-periodic function defined by $r_{p}(t)=0$ for $t\in \langle 0,p\rangle$, $r_{p}(t)=1$ for $t\in (p,2p)$ and the vector fields $\vec{v}$ and $\vec{w}$ are related by an involutive diffeomorphism.
References:
[1] W.M. Boothby: An Introduction to Differentiable Manifolds and Riemannian Geometry. Academic Press, New York, 1975. MR 0426007 | Zbl 0333.53001
[2] J.Řeháček, M. Kubíček, M. Marek: Modelling of a Tubular Catalytic Reactor with Flow Reversal. Preprint 92-001, AHPCRC, University of Minnesota, Minneapolis.
[3] C. Sparrow: The Lorenz Equations Bifurcations, Chaos and Strange Attractors. Springer-Verlag, New York, 1982. MR 0681294 | Zbl 0504.58001
[4] V. A. Pliss: Integralnye mnozhestva periodicheskikh sistem differencialnykh uravnenij. Nauka, Moscow, 1977. (Russian)
[5] J. Kurzweil: Ordinary differential equations. SNTL, Prague, 1978. (Czech) MR 0617010 | Zbl 0401.34001
[6] J. Kurzweil, O. Vejvoda: Periodicheskie resheniya sistem differencialnykh uravnenij. Czech. Math. J. 5 (1955), no. 3. (Russian) MR 0076127

Partner of