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On the limit cycles of the Floquet differential equation
1. | Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia |
2. | College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom |
References:
[1] |
V. I. Arnold, V. V. Kozlov and A. I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics, Second Printing, Springer-Verlag, Berlin, 1997. |
[2] |
A. Buică, J.P. Françoise and J. Llibre, Periodic solutions of nonlinear periodic differential systems with a small parameter, Communication on Pure and Applied Analysis, 6 (2007), 103-111.
doi: 10.1016/j.physd.2011.11.007. |
[3] |
C. Chicone, Ordinary Differential Equations with Applications, Springer-Verlag, New York, 1999. |
[4] |
D. G. de Figueiredo, Análise de Fourier e Equaçoes Diferenciais Parciais, Projeto Euclides 5, Instituto de Matemática Pura e Aplicada, Rio de Janeiro, 1977 (in Portuguese). |
[5] |
M. W. Hirsch and S. Smale, Differential Equations, Dynamical Systems and Linear Algebra, Pure and Applied Mathematics 60, Academic Press, New York, 1974. |
[6] |
J. Llibre, M.A. Teixeira and J. Torregrosa, Limit cycles bifurcating from a $k$-dimensional isochronous set center contained in $R^n$ with $k \leq n$, Math. Phys. Anal. Geom., 10 (2007), 237-249.
doi: 10.1007/s11040-007-9030-7. |
[7] |
P. Lochak and C. Meunier, Multiphase averaging for classical systems, Appl. Math. Sciences 72, Springer-Verlag, New York, 1988.
doi: 10.1007/978-1-4612-1044-3. |
[8] |
I. G. Malkin, Some Problems of the Theory of Nonlinear Oscillations, (Russian) Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1956. |
[9] |
M. Roseau, Vibrations non Linéaires et Théorie de la Stabilité, (French) Springer Tracts in Natural Philosophy, Vol.8 Springer-Verlag, Berlin-New York, 1966. |
[10] |
J. A. Sanders, F. Verhulst and J. Murdock, Averaging Methods in Nonlinear Dynamical Systems, Second edition, Applied Mathematical Sci. 59, Springer-Verlag, New York, 2007. |
[11] |
W. F. Trench, On nonautonomous linear systems of differential and difference equations with R-symmetric coefficient matrices, Linear Algebra Appl., 431 (2009), 2109-2117.
doi: 10.1016/j.laa.2009.07.004. |
[12] |
W. F. Trench, Asymptotic preconditioning of linear homogeneous systems of differential equations, Linear Algebra Appl., 434, (2011), 1631-1637.
doi: 10.1016/j.laa.2010.03.026. |
[13] |
F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Universitext, Springer-Verlag, Berlin, 1996.
doi: 10.1007/978-3-642-61453-8. |
show all references
References:
[1] |
V. I. Arnold, V. V. Kozlov and A. I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics, Second Printing, Springer-Verlag, Berlin, 1997. |
[2] |
A. Buică, J.P. Françoise and J. Llibre, Periodic solutions of nonlinear periodic differential systems with a small parameter, Communication on Pure and Applied Analysis, 6 (2007), 103-111.
doi: 10.1016/j.physd.2011.11.007. |
[3] |
C. Chicone, Ordinary Differential Equations with Applications, Springer-Verlag, New York, 1999. |
[4] |
D. G. de Figueiredo, Análise de Fourier e Equaçoes Diferenciais Parciais, Projeto Euclides 5, Instituto de Matemática Pura e Aplicada, Rio de Janeiro, 1977 (in Portuguese). |
[5] |
M. W. Hirsch and S. Smale, Differential Equations, Dynamical Systems and Linear Algebra, Pure and Applied Mathematics 60, Academic Press, New York, 1974. |
[6] |
J. Llibre, M.A. Teixeira and J. Torregrosa, Limit cycles bifurcating from a $k$-dimensional isochronous set center contained in $R^n$ with $k \leq n$, Math. Phys. Anal. Geom., 10 (2007), 237-249.
doi: 10.1007/s11040-007-9030-7. |
[7] |
P. Lochak and C. Meunier, Multiphase averaging for classical systems, Appl. Math. Sciences 72, Springer-Verlag, New York, 1988.
doi: 10.1007/978-1-4612-1044-3. |
[8] |
I. G. Malkin, Some Problems of the Theory of Nonlinear Oscillations, (Russian) Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1956. |
[9] |
M. Roseau, Vibrations non Linéaires et Théorie de la Stabilité, (French) Springer Tracts in Natural Philosophy, Vol.8 Springer-Verlag, Berlin-New York, 1966. |
[10] |
J. A. Sanders, F. Verhulst and J. Murdock, Averaging Methods in Nonlinear Dynamical Systems, Second edition, Applied Mathematical Sci. 59, Springer-Verlag, New York, 2007. |
[11] |
W. F. Trench, On nonautonomous linear systems of differential and difference equations with R-symmetric coefficient matrices, Linear Algebra Appl., 431 (2009), 2109-2117.
doi: 10.1016/j.laa.2009.07.004. |
[12] |
W. F. Trench, Asymptotic preconditioning of linear homogeneous systems of differential equations, Linear Algebra Appl., 434, (2011), 1631-1637.
doi: 10.1016/j.laa.2010.03.026. |
[13] |
F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Universitext, Springer-Verlag, Berlin, 1996.
doi: 10.1007/978-3-642-61453-8. |
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