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Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

邮发代号 80-965

2019 Impact Factor: 2.502

Frontiers of Physics  2009, Vol. 4 Issue (1): 111-121   https://doi.org/10.1007/s11467-009-0005-y
  本期目录
Classification of three-dimensional quadratic diffeomorphisms with constant Jacobian
Classification of three-dimensional quadratic diffeomorphisms with constant Jacobian
Zeraoulia ELHADJ1(), J. C. SPROTT2()
1. Department of Mathematics, University of T′ebessa, 12002, Algeria; 2. Department of Physics, University of Wisconsin, Madison, WI 53706, USA
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Abstract

The 3-D quadratic diffeomorphism is defined as a map with a constant Jacobian. A few such examples are well known. In this paper, all possible forms of the 3-D quadratic diffeomorphisms are determined. Some numerical results are also given and discussed.

Key words3-D quadratic diffeomorphism    classification    chaos
收稿日期: 2008-06-14      出版日期: 2009-03-05
Corresponding Author(s): ELHADJ Zeraoulia,Email:zeraoulia@mail.univ-tebessa.dz, zelhadj12@yahoo.fr; SPROTT J. C.,Email:sprott@physics.wisc.edu   
 引用本文:   
. Classification of three-dimensional quadratic diffeomorphisms with constant Jacobian[J]. Frontiers of Physics, 2009, 4(1): 111-121.
Zeraoulia ELHADJ, J. C. SPROTT. Classification of three-dimensional quadratic diffeomorphisms with constant Jacobian. Front. Phys. , 2009, 4(1): 111-121.
 链接本文:  
https://academic.hep.com.cn/fop/CN/10.1007/s11467-009-0005-y
https://academic.hep.com.cn/fop/CN/Y2009/V4/I1/111
1 A. L. Shilnikov, Bifurcation and chaos in the Morioka-Shimizu system, Methods of qualitative theory of differential equations (Gorky), 1986: 180-193; English translation in Selecta Math. Soviet., 1991, 10: 105-117
2 A. L. Shilnikov, Physica D , 1993, 62: 338
doi: 10.1016/0167-2789(93)90292-9
3 D. V. Turaev and L. P. Shilnikov, Sb. Math ., 1998: 189(2), 137
doi: 10.1070/SM1998v189n02ABEH000300
4 D. A. Miller and G. Grassi, A discrete generalized hyperchaotic Hénon map circuit, Circuits and Systems, MWSCAS 2001. Proceedings of the 44th IEEE 2001 Midwest Symposium 2001: 328
5 G. Baier and M. Klein, Phys. Lett. A , 1990(6-7), 151: 281
doi: 10.1016/0375-9601(90)90283-T
6 G. Grassi and S. Mascolo, A system theory approach for designing crytosystems based on hyperchaos, IEEE Transactions, Circuits & Systems-I: Fundamental theory and applications, 1999, 46(9): 1135
doi: 10.1109/81.788815
7 S. V. Gonchenko, I. I. Ovsyannikov, C. Simo, and D. Turaev, Three-Dimensional H′enon-like Maps and Wild Lorenz-like Attractors, International Journal of Bifurcation and Chaos , 2005, 15(11): 3493
doi: 10.1142/S0218127405014180
8 S. V. Gonchenko, J. D. Meiss, and I. I. Ovsyannikov, Regular and Chaotic Dynamics , 2006, 11(2): 191
doi: 10.1070/RD2006v011n02ABEH000345
9 S. V. Gonchenko and I. I. Ovsyannikov, Three-dimensional H′enon map in homoclinic bifurcations, 2005, in preparation
10 H. E. Lomeli and J. D. Meiss, Nonlinearity , 1998, 11: 557
doi: 10.1088/0951-7715/11/3/009
11 K. E. Lenz, H. E. Lomeli, and J. D. Meiss, Regular and Chaotic Motion , 1999, 3: 122
doi: 10.1070/rd1998v003n03ABEH000085
12 J. C. Sprott, Electronic Journal of Theoretical Physics , 2006, 3: 19
13 R. L. Devaney, Trans. Am. Math. Soc. , 1976, 218: 89
doi: 10.2307/1997429
14 H. Bass, E. H. Connell, and D. Wright, Bull. Amer. Math. Soc. (N.S.) , 1982, 7(2): 287
15 E. D. Courant and H. S. Snyder, Ann. Phys. (N.Y.) , 1958, 3: 1
doi: 10.1016/0003-4916(58)90012-5
16 A. J. Dragt and D. T. Abell, Symplectic maps and computation of orbits in particle accelerators. In Integration algorithms and classical mechanics ON: Toronto, 1993: 59-85 ; Amer. Math. Soc.,Providence, RI , 1996
17 E. N. Lorenz, J. Atoms. Sc. , 1963, 20: 130
18 G. Chen and X. Dong, From Chaos to Order: Methodologies, Perspectives and Applications Singapore: World Scientific , 1998
19 G. Chen, Controlling Chaos and Bifurcations in Engineering Systems, Boca Raton, FL , USA: CRC Press, 1999
20 W. W. Yu, J. Cao, K. W. Wong, and J. Lü, Chaos , 2007, 17(3): 033
21 Etienne Forest, Beam Dynamics : A New Attitude and Framework (The Physics and Technology of Particle and Photon Beams) , Amsterdam: Harwood Academic, 1998
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