Geodesic
Bifurcation of periodic and chaotic solutions in discontinuous systems
Archivum mathematicum, Tome 34 (1998) no. 1, pp. 73-82

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Chaos generated by the existence of Smale horseshoe is the well-known phenomenon in the theory of dynamical systems. The Poincaré-Andronov-Melnikov periodic and subharmonic bifurcations are also classical results in this theory. The purpose of this note is to extend those results to ordinary differential equations with multivalued perturbations. We present several examples based on our recent achievements in this direction. Singularly perturbed problems are studied as well. Applications are given to ordinary differential equations with both dry friction and relay hysteresis terms.
Classification : 34A60, 34C23, 34C25, 34E15, 37D45, 37J40, 58F13
Keywords: Chaotic and periodic solutions; differential inclusions; relay hysteresis 
@article{ARM_1998__34_1_a7,
     author = {Fe\v{c}kan, Michal},
     title = {Bifurcation of periodic and chaotic solutions in discontinuous systems},
     journal = {Archivum mathematicum},
     pages = {73--82},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {1998},
     mrnumber = {1629664},
     zbl = {0914.34039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1998__34_1_a7/}
}
TY  - JOUR
AU  - Fečkan, Michal
TI  - Bifurcation of periodic and chaotic solutions in discontinuous systems
JO  - Archivum mathematicum
PY  - 1998
SP  - 73
EP  - 82
VL  - 34
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ARM_1998__34_1_a7/
LA  - en
ID  - ARM_1998__34_1_a7
ER  - 
%0 Journal Article
%A Fečkan, Michal
%T Bifurcation of periodic and chaotic solutions in discontinuous systems
%J Archivum mathematicum
%D 1998
%P 73-82
%V 34
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ARM_1998__34_1_a7/
%G en
%F ARM_1998__34_1_a7
Fečkan, Michal. Bifurcation of periodic and chaotic solutions in discontinuous systems. Archivum mathematicum, Tome 34 (1998) no. 1, pp. 73-82. http://geodesic.mathdoc.fr/item/ARM_1998__34_1_a7/