On singularly perturbed ordinary differential equations with measure-valued limits

Zvi Artstein

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 2, page 139-152
  • ISSN: 0862-7959

Abstract

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The limit behaviour of solutions of a singularly perturbed system is examined in the case where the fast flow need not converge to a stationary point. The topological convergence as well as information about the distribution of the values of the solutions can be determined in the case that the support of the limit invariant measure of the fast flow is an asymptotically stable attractor.

How to cite

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Artstein, Zvi. "On singularly perturbed ordinary differential equations with measure-valued limits." Mathematica Bohemica 127.2 (2002): 139-152. <http://eudml.org/doc/249047>.

@article{Artstein2002,
abstract = {The limit behaviour of solutions of a singularly perturbed system is examined in the case where the fast flow need not converge to a stationary point. The topological convergence as well as information about the distribution of the values of the solutions can be determined in the case that the support of the limit invariant measure of the fast flow is an asymptotically stable attractor.},
author = {Artstein, Zvi},
journal = {Mathematica Bohemica},
keywords = {singular perturbations; invariant measures; slow and fast motions; singular perturbations; invariant measures; slow and fast motions},
language = {eng},
number = {2},
pages = {139-152},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On singularly perturbed ordinary differential equations with measure-valued limits},
url = {http://eudml.org/doc/249047},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Artstein, Zvi
TI - On singularly perturbed ordinary differential equations with measure-valued limits
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 2
SP - 139
EP - 152
AB - The limit behaviour of solutions of a singularly perturbed system is examined in the case where the fast flow need not converge to a stationary point. The topological convergence as well as information about the distribution of the values of the solutions can be determined in the case that the support of the limit invariant measure of the fast flow is an asymptotically stable attractor.
LA - eng
KW - singular perturbations; invariant measures; slow and fast motions; singular perturbations; invariant measures; slow and fast motions
UR - http://eudml.org/doc/249047
ER -

References

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  10. Systems of differential equations containing small parameters in the derivative, Mat. Sbornik N. S. 31 (1952), 575–586. (1952) MR0055515
  11. 10.1007/978-3-642-82175-2_3, Springer, Berlin, 1985. (1985) MR0788499DOI10.1007/978-3-642-82175-2_3
  12. On the flow outside a closed invariant set; stability, relative stability and saddle sets, Contrib. Differential Equations 3 (1964), 249–294. (1964) Zbl0161.28803MR0163018
  13. Asymptotic Expansions for Ordinary Differential Equations, Wiley Interscience, New York, 1965. (1965) Zbl0133.35301MR0203188
  14. Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, Springer, New York, 1975. (1975) Zbl0304.34051MR0466797

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