YANG Jing^{1,2}, YANG Ming^{1,2}, LU Zhengyi^{3}
[1] Birkhoff G D, The restricted problem of three bodies, Rendiconti del Circolo Matematico di Palermo (18841940), 1915, 39(1): 265334. [2] Devaney R L, Reversible diffeomorphismas and flows, Trans. Amer. Math. Soc., 1976, 218: 89113. [3] Romanovski V G and Shafer D S, The Center and Cyclicity Problems: A Computational Algebra Approach, Springer, Boston, 2009. [4] Giné J and Maza S, The reversibility and the center problem, Nonl. Anal. TMA, 2011, 74(2): 695704. [5] Dukarić M, Giné J, and Llibre J, Reversible nilpotent centers with cubic homogeneous nonlinearities, Journal of Mathematical Analysis and Applications, 2016, 433(1): 305319. [6] Buzzi C A, Llibre J, and Medrado J C R, Phase portraits of reversible linear differential systems with cubic homogeneous polynomial nonlinearities having a nondegenerate center at the origin, Qual. Theory Dyn. Syst., 2009, 7(2): 369403. [7] Boros B, Hofbauer J, Müller S, et al., The center problem for the Lotka reactions with generalized massaction kinetics, Qual. Theory Dyn. Syst., 2018, 17(2): 403410. [8] Han M, Petek T, and Romanovski V G, Reversibility in polynomial systems of ODE's, Appl. Math. Comput., 2018, 338: 5571. [9] Cox D A, Little J, and O'Shea D, Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, Undergraduate Texts in Mathematics, Springer, New York, 4th ed., 2015. [10] Yang J, Yang M, and Lu Z, The center problems and timereversibility with respect to a linear involution, Mathematica Applicata, 2021, 34(1): 3746. [11] Pearson J M, Lloyd N G, and Christopher C J, Algorithmic derivation of centre conditions, SIAM Review, 1996, 38(4): 619636. [12] Poincaré H, Les Méthodes Nouvelles Mécanique Céleste, vol. 1, GauthierVillars, Paris, 1892. [13] Teixeira M A and Yang J, The centerfocus problem and reversibility, J. Differential Equations, 2001, 174(1): 237251. [14] Ritt J F. Differential Algebra, vol. 33 of Colloquium Publications, American Mathematical Society, Providence, 1950. [15] Wu W T, On the decision problem and the mechanization of theoremproving in elementary geometry, Sci. Chin. (A), 1978, XXI(2): 159172. [16] Buchberger B, Ein algorithmus zum auffinden der basiselemente des restklassenrings nach einem nulldimensionalen polynomideal, Ph.D. thesis, University of Innsbruck, 1965. [17] Kalkbrener M, Three contributions to elimination theory, Ph.D. thesis, Johannes Kepler Universität Linz, Linz, 1991. [18] Yang L and Zhang J, Searching dependency between algebraic equations: An algorithm applied to automated reasoning, Tech. Rep., International Centre for Theoretical Physics, Trieste, 1991. [19] Chen C, Davenport J H, May J P, et al., Triangular decomposition of semialgebraic systems, J. Symb. Comput., 2013, 49: 326. [20] Zwillinger D, CRC Standard Mathematical Tables and Formulas, 32nd ed., CRC Press, New York, 2012. 
[1]  Yuqiong DING, Yonghai LI. FINITE VOLUME ELEMENT METHOD WITH LAGRANGIAN CUBIC FUNCTIONS [J]. Journal of Systems Science and Complexity, 2011, 24(5): 9911006. 
[2]  Xiaoguang YANG ;Jianzhong ZHANG . INVERSE CENTER LOCATION PROBLEM ON A TREE [J]. Journal of Systems Science and Complexity, 2008, 21(4): 651664. 
[3]  Dai Zhan CHENG. ON COMPLEX DYNAMIC CONTROL SYSTEMS [J]. Journal of Systems Science and Complexity, 2003, 16(3): 350357. 
[4]  Min CHEN;Guo Fu WU;Gemai Chen. A NEW TEST FOR NORMALITY IN LINEAR AUTOREGRESSIVE MODELS [J]. Journal of Systems Science and Complexity, 2002, 15(4): 423435. 
[5]  Yi Guang HONG;Dai Zhan CHEN;Hua Shu QIN. STABILIZATION OF NONLINEAR SYSTEMS WITH HOMOGENEOUS STABILITY [J]. Journal of Systems Science and Complexity, 1999, 12(Supplement): 104109. 
[6]  Cheng Daizhan. STATE FEEDBACK STABILIZATION OF PLANE SYSTEMS [J]. Journal of Systems Science and Complexity, 1990, 1(4): 375380. 
Viewed  
Full text 


Abstract 

