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

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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 
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     author = {Fe\v{c}kan, Michal},
     title = {Bifurcation of periodic and chaotic solutions in discontinuous systems},
     journal = {Archivum mathematicum},
     pages = {73--82},
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     volume = {34},
     number = {1},
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     zbl = {0914.34039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1998__34_1_a7/}
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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/