The Structure of Reflective Function of Higher Dimensional Differential System

Author(s)
Zhengxin Zhou

ABSTRACT

In this article, we discuss the structure of reflective function of the higher dimensional differential systems and apply the results to study the existence of periodic solutions of these systems.

In this article, we discuss the structure of reflective function of the higher dimensional differential systems and apply the results to study the existence of periodic solutions of these systems.

Cite this paper

nullZ. Zhou, "The Structure of Reflective Function of Higher Dimensional Differential System,"*Applied Mathematics*, Vol. 1 No. 1, 2010, pp. 76-80. doi: 10.4236/am.2010.11009.

nullZ. Zhou, "The Structure of Reflective Function of Higher Dimensional Differential System,"

References

[1] V. I. Arnold, “Ordinary Differential Equation,” Science Press, Moscow, 1971, pp. 198-240.

[2] V. I. Mironenko, “Reflective Function and Periodic Solu-tion of the Differential System,” University Press, Minsk, 1986, pp. 12-26.

[3] V. I. Mironenko, “The Reflecting Function and Integral Manifolds of Differential Systems,” Differential Equations, Vol. 28, No. 6, 1992, pp. 984-991.

[4] V. V. Mironenko, “Time Symmetry Preserving Perturba-tions of Differential Systems,” Differential Equations, Vol. 40, No. 20, 2004, pp. 1395-1403.

[5] P. P. Verecovich, “Nonautonomous Second Order Quadric Wystem Equivalent to Linear System,” Differential Equations, Vol. 34, No. 12, 1998, pp. 2257-2259.

[6] E. V. Musafirov, “Differential Systems, the Mapping over Period for Which is Represented by a Product of Three Exponential Matrixes,” Journal of Mathematical Analysis and Applications, Vol. 329, No.1, 2007, pp. 647-654.

[7] Z. X. Zhou, “On the Reflective Function of Polynomial Differential System,” Journal of Mathematical Analysis and Applications, Vol. 278, No. 1, 2003, pp. 18-26.

[8] Z. X. Zhou and Y. X. Yan, “Reflecting Function and Periodic Solution of Quadratic Differential Sys-tem,” Applied Mathematics, Vol. 15, No. 4, 2002, pp. 85-91.

[1] V. I. Arnold, “Ordinary Differential Equation,” Science Press, Moscow, 1971, pp. 198-240.

[2] V. I. Mironenko, “Reflective Function and Periodic Solu-tion of the Differential System,” University Press, Minsk, 1986, pp. 12-26.

[3] V. I. Mironenko, “The Reflecting Function and Integral Manifolds of Differential Systems,” Differential Equations, Vol. 28, No. 6, 1992, pp. 984-991.

[4] V. V. Mironenko, “Time Symmetry Preserving Perturba-tions of Differential Systems,” Differential Equations, Vol. 40, No. 20, 2004, pp. 1395-1403.

[5] P. P. Verecovich, “Nonautonomous Second Order Quadric Wystem Equivalent to Linear System,” Differential Equations, Vol. 34, No. 12, 1998, pp. 2257-2259.

[6] E. V. Musafirov, “Differential Systems, the Mapping over Period for Which is Represented by a Product of Three Exponential Matrixes,” Journal of Mathematical Analysis and Applications, Vol. 329, No.1, 2007, pp. 647-654.

[7] Z. X. Zhou, “On the Reflective Function of Polynomial Differential System,” Journal of Mathematical Analysis and Applications, Vol. 278, No. 1, 2003, pp. 18-26.

[8] Z. X. Zhou and Y. X. Yan, “Reflecting Function and Periodic Solution of Quadratic Differential Sys-tem,” Applied Mathematics, Vol. 15, No. 4, 2002, pp. 85-91.