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	1. Chaos Criterion Theorems on Specific 2n Order and 2n + 1 Order Polynomial Discrete Maps with Application
	Chu Jixun,Min Lequan
	Mathematics 29 December 2019
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	Abstract:Li and Yorke's seminal paper published in 1975 has provided a criterion for the existence of chaos in one-dimensional difference equations. Generally speaking, it is difficult to use this criterion to verify whether a high order polynomial discrete mapping is chaotic. Because one needs to solve several high order polynomial equations on the polynomial parameters. Firstly, this paper introduces two theorems of the existence of chaos on two kinds of specific 2n order and 2n+1 order polynomial discrete mappings. These two theorems provide chaotic parameter intervals of the specific polynomials, which satisfy the Li-Yorke criterion. Secondly, four examples are presented to verify the effectiveness of the theorems. Thirdly, by using a generalized synchronization theorem and the chaos mappings given in the four examples, a new 8-dimensional chaotic generalized synchronization system (8DCGSS) is constructed. Then a chaotic PRNG (CPRNG) is designed. The keyspace of the CPRNG is larger than 2^1117. Finally, by using the FIPS 140-2 randomness test and a generalized FIPS 140-2 randomness test, the randomness of the keystreams generated via the CPRNG is measured. The results show that the CPRNG is able to generate sound pseudorandom keystreams.
	TO cite this article:Chu Jixun,Min Lequan. Chaos Criterion Theorems on Specific 2n Order and 2n + 1 Order Polynomial Discrete Maps with Application[OL].[29 December 2019] http://en.paper.edu.cn/en_releasepaper/content/4750298


	2. Long time stability of solutions for the fourth order nonlinear Schrödinger equation
	GAO Meina,LIU Jianjun
	Mathematics 28 May 2018
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	Abstract:In this paper, a long time stability result is proved is proved for the cubic fourth order nonlinear Schrödinger equation with periodic boundary conditions$$\mathbf{i}u_t=\partial_x^4u\pm\|u\|^2u,\hspace{12pt}x\in\mathbb{T}:=\mathbb{R}/2\pi\mathbb{Z}.$$
	TO cite this article:GAO Meina,LIU Jianjun. Long time stability of solutions for the fourth order nonlinear Schrödinger equation[OL].[28 May 2018] http://en.paper.edu.cn/en_releasepaper/content/4745259


	3. Quasi-periodic solutions for the fourth order nonlinear Schr$\ddot{\mbox{o}}$dinger equation
	GAO Meina,LIU Jianjun
	Mathematics 15 May 2018
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	Abstract:This paper is concerned with the cubic fourth order nonlinearSchr$\ddot{\mbox{o}}$dinger equation with periodic boundary conditions$$\mathbf{i}u_t=\partial_x^4u\pm\|u\|^2u,\hspace{12pt}x\in\mathbb{T}:=\mathbb{R}/2\pi\mathbb{Z}.$$We show the above equation possesses Cantor families of quasi-periodic solutions of small amplitude.
	TO cite this article:GAO Meina,LIU Jianjun. Quasi-periodic solutions for the fourth order nonlinear Schr$\ddot{\mbox{o}}$dinger equation[OL].[15 May 2018] http://en.paper.edu.cn/en_releasepaper/content/4744994


	4. Variational approach toa class of second order Hamiltonian systems with impulsiveeffects
	ZHOU Jian-Wen,WANG Yan-Ning
	Mathematics 06 November 2015
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	Abstract:In this paper, we present a recent approach via variational methodsand critical point theory to obtain the existence and multiplicityof periodic solutions for the second order Hamiltonian system withimpulsive effects. By establishing a proper variational setting,one multiplicity results is obtained.Finally, one examples is presented to illustrate the feasibilityand effectiveness of our results.
	TO cite this article:ZHOU Jian-Wen,WANG Yan-Ning. Variational approach toa class of second order Hamiltonian systems with impulsiveeffects[OL].[ 6 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4660449


	5. Invariant algebraic surfaces of the Chen system
	Deng Xijun ,Aiyong Chen
	Mathematics 04 May 2010
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	Abstract:In this paper, enlightened by the idea of the weight of a polynomial introduced by Peter Swinnerton-dyer [Peter Swinnerton-dyer, The invariant algebraic surfaces of the Lorenz system, Math.Proc.Camb.Phil.Soc. (2002), 132,385-393.], we find all the invariant algebraic surfaces of the Chen system x\
	TO cite this article:Deng Xijun ,Aiyong Chen. Invariant algebraic surfaces of the Chen system[OL].[ 4 May 2010] http://en.paper.edu.cn/en_releasepaper/content/42530


	6. 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


	7. New Periodic Solutions for the Circular Restricted 3-Body and 4-Body Problems
	Zhang Shiqing,Yin Qunyao
	Mathematics 24 February 2009
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	Abstract:For the circular restricted 3-body and 4-body problems in R^2, we prove the existence of new symmetric noncollision periodic solutions with some fixed winding numbers and masses.Our results should be useful in celestial mechanics.
	TO cite this article:Zhang Shiqing,Yin Qunyao. New Periodic Solutions for the Circular Restricted 3-Body and 4-Body Problems[OL].[24 February 2009] http://en.paper.edu.cn/en_releasepaper/content/29566

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