| Title:
|
On systems governed by two alternating vector fields (English) |
| Author:
|
Klíč, Alois |
| Author:
|
Řeháček, Jan |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
1994 |
| Pages:
|
57-64 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
periodic system |
| Keyword:
|
period map |
| Keyword:
|
invariant set |
| Keyword:
|
flow |
| MSC:
|
34A34 |
| MSC:
|
34C25 |
| MSC:
|
58F08 |
| idZBL:
|
Zbl 0797.34047 |
| idMR:
|
MR1254747 |
| DOI:
|
10.21136/AM.1994.134243 |
| . |
| Date available:
|
2009-09-22T17:42:45Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134243 |
| . |
| Reference:
|
[1] W.M. Boothby: An Introduction to Differentiable Manifolds and Riemannian Geometry.Academic Press, New York, 1975. Zbl 0333.53001, MR 0426007 |
| Reference:
|
[2] J.Řeháček, M. Kubíček, M. Marek: Modelling of a Tubular Catalytic Reactor with Flow Reversal.Preprint 92-001, AHPCRC, University of Minnesota, Minneapolis. |
| Reference:
|
[3] C. Sparrow: The Lorenz Equations Bifurcations, Chaos and Strange Attractors.Springer-Verlag, New York, 1982. Zbl 0504.58001, MR 0681294 |
| Reference:
|
[4] V. A. Pliss: Integralnye mnozhestva periodicheskikh sistem differencialnykh uravnenij.Nauka, Moscow, 1977. (Russian) |
| Reference:
|
[5] J. Kurzweil: Ordinary differential equations.SNTL, Prague, 1978. (Czech) Zbl 0401.34001, MR 0617010 |
| Reference:
|
[6] J. Kurzweil, O. Vejvoda: Periodicheskie resheniya sistem differencialnykh uravnenij.Czech. Math. J. 5 (1955), no. 3. (Russian) MR 0076127 |
| . |
