Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 275, pp. 1-10.
Oscillations with one degree of freedom and discontinuous energy
Miguel V. S. Frasson, Marta C. Gadotti,
Selma H. J. Nicola, Placido Z. Taboas
Abstract:
In 1995 for a linear oscillator, Myshkis imposed a constant impulse
to the velocity, each moment the energy reaches a certain level. The
main feature of the resulting system is that it defines a nonlinear
discontinuous semigroup. In this note we study the orbital stability
of a one-parameter family of periodic solutions and state the
existence of a period-doubling bifurcation of such solutions.
Submitted September 30, 2015. Published October 23, 2015.
Math Subject Classifications: 34C25, 34D20, 37G15.
Key Words: Periodic solutions; discontinuous energy;
orbital stability; bifurcation.
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Miguel V. S. Frasson
Departamento de Matemática Aplicada e Estatística
ICMC-Universidade de São Paulo
Avenida Trabalhador São-carlense 400
13566-590 São Carlos SP, Brazil
email: frasson@icmc.usp.br
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Marta C. Gadotti
Departamento de Matemática
IGCE - Universidade Estadual Paulista
Avenida 24A 1515,
13506-700 Rio Claro SP, Brazil
email: martacg@rc.unesp.br
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Selma H. J. Nicola
Departamento de Matemática
Universidade Federal de São Carlos
Rodovia Washington Luis, km 235 Norte
13565-905 São Carlos SP, Brazil
email: selmaj@dm.ufscar.br
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Plácido Z. Táboas
Departamento de Matemática Aplicada e Estatística
ICMC-Universidade de São Paulo
Avenida Trabalhador São-carlense 400
13566-590 São Carlos SP, Brazil
email: pztaboas@icmc.usp.br
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