On systems governed by two alternating vector fields

Alois Klíč; Jan Řeháček

Applications of Mathematics (1994)

  • Volume: 39, Issue: 1, page 57-64
  • ISSN: 0862-7940

Abstract

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We investigate the nonautonomous periodic system of ODE’s of the form , where is a -periodic function defined by for , for and the vector fields and are related by an involutive diffeomorphism.

How to cite

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Klíč, Alois, and Řeháček, Jan. "On systems governed by two alternating vector fields." Applications of Mathematics 39.1 (1994): 57-64. <http://eudml.org/doc/32869>.

@article{Klíč1994,
abstract = {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.},
author = {Klíč, Alois, Řeháček, Jan},
journal = {Applications of Mathematics},
keywords = {periodic system; period map; invariant set; flow; alternating vector fields; involutive diffeomorphism; tabular catalytic reactor; periodic orbits; measure property of bounded invariant sets},
language = {eng},
number = {1},
pages = {57-64},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On systems governed by two alternating vector fields},
url = {http://eudml.org/doc/32869},
volume = {39},
year = {1994},
}

TY - JOUR
AU - Klíč, Alois
AU - Řeháček, Jan
TI - On systems governed by two alternating vector fields
JO - Applications of Mathematics
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 39
IS - 1
SP - 57
EP - 64
AB - 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.
LA - eng
KW - periodic system; period map; invariant set; flow; alternating vector fields; involutive diffeomorphism; tabular catalytic reactor; periodic orbits; measure property of bounded invariant sets
UR - http://eudml.org/doc/32869
ER -

References

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  1. An Introduction to Differentiable Manifolds and Riemannian Geometry, Academic Press, New York, 1975. (1975) Zbl0333.53001MR0426007
  2. Modelling of a Tubular Catalytic Reactor with Flow Reversal, Preprint 92-001, AHPCRC, University of Minnesota, Minneapolis. 
  3. The Lorenz Equations Bifurcations, Chaos and Strange Attractors, Springer-Verlag, New York, 1982. (1982) Zbl0504.58001MR0681294
  4. Integralnye mnozhestva periodicheskikh sistem differencialnykh uravnenij, Nauka, Moscow, 1977. (Russian) (1977) 
  5. Ordinary differential equations, SNTL, Prague, 1978. (Czech) (1978) Zbl0401.34001MR0617010
  6. Periodicheskie resheniya sistem differencialnykh uravnenij, Czech. Math. J. 5 (1955), no. 3. (Russian) (1955) MR0076127

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