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	1. A Singular algorithm for polynomial iterative roots
	YU Zhiheng, ZHANG Weinian
	Mathematics 24 May 2016
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	Abstract:Based on the theory of minimal irreducible decomposition and thecomputer algebra system {it Singular}, we give an algorithm which can be used to find the simplest algebraicrelations among coefficients polynomials of degree $m^n$ for these polynomials having the $n$-th iterative roots of polynomial form.Moreover, using the algorithm, the explicit expressions of the iterative roots will be given.Furthermore, applying the algorithm we obtain the polynomial quadratic iterative roots of polynomialsof degree 9 and 16.
	TO cite this article:YU Zhiheng, ZHANG Weinian. A Singular algorithm for polynomial iterative roots[OL].[24 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4693828


	2. Centering Conditions for the Poincar'{e} Systems $P(2,12) $ with a Uniformly Isochronous Center
	XU Jin-Ya, LU Zheng-Yi
	Mathematics 31 December 2014
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	Abstract:We obtain sufficient and necessary centering conditions for the Poincar'e system $P(2,12)$. The necessity of the condition is derived from the first twelve focal values by symbolic computation with Maple, and the sufficiency is proved by verifying the reversibility of the system.
	TO cite this article:XU Jin-Ya, LU Zheng-Yi. Centering Conditions for the Poincar'{e} Systems $P(2,12) $ with a Uniformly Isochronous Center[OL].[31 December 2014] http://en.paper.edu.cn/en_releasepaper/content/4626244

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	3. Gevrey regularity of invariant curves ofanalytic area preserving mappings
	ZHANG Dongfeng
	Mathematics 08 January 2012
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	Abstract:In this paper we prove the existence of aGevrey family of invariant curves for analytic area preserving mappings.The Gevrey smoothness is expressedby Gevrey index. we specifically obtain the Gevreyindex of invariant curve which is related to smoothness ofarea preserving mapping and the exponent of the smalldivisors condition. Moreover, weobtain a Gevrey normal form of the area preserving mappings in aneighborhood of the union of the invariantcurves.
	TO cite this article:ZHANG Dongfeng. Gevrey regularity of invariant curves ofanalytic area preserving mappings[OL].[ 8 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4460611


	4. On invariant curves ofanalytic non-twist area preserving mappings
	ZHANG Dongfeng
	Mathematics 06 January 2012
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	Abstract:In this paper we consider small perturbation of analytic non-twistarea preserving mappings, and prove the existence of invariantcurve by KAM iteration. As we know if the twist condition is not satisfied, the frequency of invariant curve may have some drift. But in this paper, we prove that the frequency of invariant curve persists without any drift.
	TO cite this article:ZHANG Dongfeng. On invariant curves ofanalytic non-twist area preserving mappings[OL].[ 6 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4460285


	5. Uniform Exponential Attractor For Nonautonomous Partly DissipativeLattice Dynamical System
	ZHOU Sheng-Fan, Lou Jia-Jia
	Mathematics 04 January 2012
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	Abstract:In this paper, we consider the existence of auniform exponential attractor for the nonautonomous partly dissipativelattice dynamical system with quasiperiodic external forces. First we prove the existence and uniqueness of solutions and the solution mapping generates a continuous process on the phase space. Second we consider the uniformly boundedness of the solutions and the existence of a bounded absorbing set. Then we prove the Lipschitz property of solutions and obtain the estimation between two solutions by the method of ``end estimate". Finally we get the existence of a uniform exponential attractor for the continuous process associated with the considered system.
	TO cite this article:ZHOU Sheng-Fan, Lou Jia-Jia. Uniform Exponential Attractor For Nonautonomous Partly DissipativeLattice Dynamical System[OL].[ 4 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4459738


	6. Stability of Iterative Roots
	ZHANG Weinian
	Mathematics 02 January 2012
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	Abstract:Since many results on existence of continuous iterative roots were obtained, stability of iterative roots becomes an important subject in order to compute iterative roots numerically. This paper discusses on continuous stability and continuously differentiable stability of monotone iterative roots, showing results of the Hyers-Ulam stability, results of approximation which actually give continuous stability, and a comparison between local continuously differentiable stablility and global continuously differentiable unstability for iterative roots.
	TO cite this article:ZHANG Weinian. Stability of Iterative Roots[OL].[ 2 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4459195


	7. Modified projective synchronization of fractional-order chaotic systems with different dimensions
	WU Ranchao,ZHANG Xi
	Mathematics 28 March 2011
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	Abstract:In this letter, the modified projective synchronization between two fractional-order chaotic systems with different dimensions is investigated. The added-order scheme and the reduced-order scheme are proposed, respectively. Based on the Laplace transformation and feedback control theory, controllers are designed such that two chaotic systems with different dimensions could be synchronized asymptotically under the presented schemes. Corresponding numerical simulations are given to show the effectiveness of the proposed schemes.
	TO cite this article:WU Ranchao,ZHANG Xi. Modified projective synchronization of fractional-order chaotic systems with different dimensions[OL].[28 March 2011] http://en.paper.edu.cn/en_releasepaper/content/4418807


	8. Quasi-periodic Solutions for 2k Order Wave Equations
	Gao Yixian,Chang Jing
	Mathematics 22 March 2011
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	Abstract:In this paper, we consider one-dimensional (1D) nonlinear 2k order wave equations under the Dirichlet boundary conditions, weher the nonlinearity f is an analytic, odd function. It is proved that for almost all real pa-rameters m>0, the equations admit small-amplitude quasi-periodic solutionscorresponding to finite dimensional invariant tori for an associated infnite dimensional dynamical system. The proof is based on an infnite dimensional KAM theory and apartial Birkhoff normal form technique.
	TO cite this article:Gao Yixian,Chang Jing. Quasi-periodic Solutions for 2k Order Wave Equations[OL].[22 March 2011] http://en.paper.edu.cn/en_releasepaper/content/4417792


	9. Centers and bifurcations of a switching quadratic system
	CHEN Xingwu
	Mathematics 18 March 2011
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	Abstract:In this paper we study the center problem and the limit cycle bifurcation of switching differential systems. Computing the generalized Lyapunov constants and decomposing their variety, we obtain the center condition of a switching quadratic system. Moreover, developing Christopher's method of finding limit cycles near centers for analytic systems, we prove that there are perturbations having 9 limit cycles near the center at the origin of the considered switching quadratic system.
	TO cite this article:CHEN Xingwu. Centers and bifurcations of a switching quadratic system[OL].[18 March 2011] http://en.paper.edu.cn/en_releasepaper/content/4417051


	10. Notes on a Theorem of Benci-Gluck-Ziller-Hayashi
	Zhang Shiqing
	Mathematics 27 September 2009
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	Abstract:We use constrained variational minimizing methods to study the existence of periodic solutions with a prescribed energy for a class of second order Hamiltonian systems with C^2 potential V function which has an unbounded upper level set, our result can be regarded as a complementary of the well-known Theorem of Benci-Gluck-Ziller and Hayashi.
	TO cite this article:Zhang Shiqing. Notes on a Theorem of Benci-Gluck-Ziller-Hayashi[OL].[27 September 2009] http://en.paper.edu.cn/en_releasepaper/content/35509

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