Linearizability conditions of a time-reversible quartic-like system

In this paper we study the linearizability problem of polynomial-like complex differential systems. We give a reduction of linearizability problem of such non-polynomial systems to the problem of polynomial systems. Applying this reduction, we find some linearizability conditions for a time-reversible quartic-like complex system and derive from them conditions of isochronous center for the corresponding real system.

[1]  J. Lamb,et al.  Time-reversal symmetry in dynamical systems: a survey , 1998 .

[2]  Christiane Rousseau,et al.  Linearization of Isochronous Centers , 1995 .

[3]  Kenichiro Aoki,et al.  Time-reversible deterministic thermostats , 2004 .

[4]  J. Lamb,et al.  On symmetric attractors in reversible dynamical systems , 1998 .

[5]  Valery G. Romanovski,et al.  Linearizability conditions of time-reversible quartic systems having homogeneous nonlinearities , 2008 .

[6]  Valery G. Romanovski,et al.  Linearizability conditions of time-reversible cubic systems , 2010 .

[7]  M. Matveyev.  Reversible systems with first integrals , 1998 .

[8]  Valery G. Romanovski,et al.  Linearizability of linear systems perturbed by fifth degree homogeneous polynomials , 2007 .

[9]  Jaume Giné,et al.  Isochronous centers of a linear center perturbed by fourth degree homogeneous polynomial , 1999 .

[10]  Christiane Rousseau,et al.  Normalizable, Integrable, and Linearizable Saddle Points for Complex Quadratic Systems in $$\mathbb{C}^2 $$ , 2003 .

[11]  M. Irwin,et al.  Smooth Dynamical Systems , 2001 .

[12]  C. Rousseau,et al.  Nondegenerate linearizable centres of complex planar quadratic and symmetric cubic systems in $\mathbb{C}^2$ , 2001 .

[13]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[14]  Jaume Llibre,et al.  Classification of the centers, their cyclicity and isochronicity for the generalized quadratic polynomial differential systems , 2009 .

[15]  Valery G. Romanovski,et al.  The Center and Cyclicity Problems: A Computational Algebra Approach , 2009 .

[16]  Jaume Llibre,et al.  Classification of the centers, their cyclicity and isochronicity for a class of polynomial differential systems generalizing the linear systems with cubic homogeneous nonlinearities , 2009 .

[17]  Wentao Huang,et al.  A new method to determine isochronous center conditions for polynomial differential systems , 2003 .

[18]  Jaume Llibre,et al.  Classification of the centers and isochronous centers for a class of quartic-like systems , 2009 .

[19]  Valery G. Romanovski,et al.  Time-Reversibility in 2-Dimensional Systems , 2008, Open Syst. Inf. Dyn..

[20]  Time reversibility in nonequilibrium thermomechanics , 1998 .

[21]  Konstantin Sergeevich Sibirsky.  Introduction to the Algebraic Theory of Invariants of Differential Equations , 1989 .

[22]  Liu Yi-Reng,et al.  THEORY OF VALUES OF SINGULAR POINT IN COMPLEX AUTONOMOUS DIFFERENTIAL SYSTEMS , 1990 .

[23]  C. Lim,et al.  Time-reversible and equivariant pitchfork bifurcation , 1998 .

[24]  Marco Sabatini,et al.  A survey of isochronous centers , 1999 .