Leonardo Laura-Guarachi, Osvaldo Osuna, Gabriel Villasenor-Aguilar
Abstract:
It is known that if a planar differential systems has an inverse
integrating factor, then all the limit cycles contained in the domain
of definition of the inverse integrating factor are contained in
the zero set of this function. Using this fact we give some
criteria to rule out the existence of limit cycles.
We also present some applications and examples that illustrate our
results.
Submitted September 1, 2011. Published September 27, 2011.
Math Subject Classifications: 34C05, 34C07, 34C25.
Key Words: Algebraic set; integrating factors;
inverse integrating factors; limit cycles.
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Leonardo Laura-Guarachi Instituto de Física y Matemáticas Universidad Michoacana, Edif. C-3, Cd. Universitaria C.P. 58040. Morelia, Mich., México email: leonardo@ifm.umich.mx |
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Osvaldo Osuna Instituto de Física y Matemáticas Universidad Michoacana, Edif. C-3, Cd. Universitaria C.P. 58040. Morelia, Mich., México email: osvaldo@ifm.umich.mx |
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Gabriel Villaseñor-Aguilar Instituto de Física y Matemáticas Universidad Michoacana, Edif. C-3, Cd. Universitaria C.P. 58040. Morelia, Mich., México email: gabriel@ifm.umich.mx |
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