CRITICAL PERIODS OF THIRD-ORDER PLANAR HAMILTONIAN SYSTEMS

被引：15
|
作者：
Yu, Pei [1 ,2 ]
Han, Maoan [1 ]
Zhang, Jizhou [1 ]
机构：
[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
[2] Univ Western Ontario, Dept Appl Math, London, ON N6A 5B7, Canada
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2010年 / 20卷 / 07期
基金：
加拿大自然科学与工程研究理事会; 中国国家自然科学基金;
关键词：
Critical periods; Hamiltonian system; center; normal form; HILBERTS 16TH PROBLEM; 12; LIMIT-CYCLES; VECTOR-FIELDS; CUBIC SYSTEMS; BIFURCATION; COMPUTATION;
D O I：
10.1142/S0218127410027040
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper considers the critical periods of third-order planar Hamiltonian systems. It is assumed that the origin of the system is a center. With the aid of symbolic and numerical computations, we show the existence of seven local critical periods. This is the maximal number of local critical periods that a cubic Hamiltonian system can have.
引用
收藏
页码：2213 / 2224
页数：12
相关论文
共 50 条
  • [21] MODES IN THIRD-ORDER PERIODICALLY SWITCHED SYSTEMS
    KEENAN, RK
    PROCEEDINGS OF THE IEEE, 1969, 57 (11) : 2077 - &
  • [22] Continuous Twisting Algorithm for Third-Order Systems
    Mendoza-Avila, Jesus
    Moreno, Jaime A.
    Fridman, Leonid M.
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2020, 65 (07) : 2814 - 2825
  • [23] Practical stabilization of third-order bilinear systems
    A. E. Golubev
    A. P. Krishchenko
    Differential Equations, 2015, 51 : 1092 - 1096
  • [24] On third-order bilinear systems in the degenerate case
    Berezkina, NS
    Martynov, IP
    Pronko, VA
    DIFFERENTIAL EQUATIONS, 1995, 31 (12) : 2046 - 2048
  • [25] Robust Stability of Third-Order Control Systems
    Aleksandrov, V. V.
    Zueva, I. O.
    Sidorenko, G. Yu.
    MOSCOW UNIVERSITY MECHANICS BULLETIN, 2014, 69 (01) : 10 - 15
  • [26] Superintegrable systems with third-order integrals of motion
    Marquette, Ian
    Winternitz, Pavel
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2008, 41 (30)
  • [27] Suppression of third-order intermodulation in a klystron by third-order injection
    Bhattacharjee, S
    Marchewka, C
    Welter, J
    Kowalczyk, R
    Wilsen, CB
    Lau, YY
    Booske, JH
    Singh, A
    Scharer, JE
    Gilgenbach, RM
    Neumann, MJ
    Keyser, MW
    PHYSICAL REVIEW LETTERS, 2003, 90 (09)
  • [28] Informative Order-Reduction of Underdamped Third-Order Systems
    Albatran, Saher
    Alatoum, Ammar
    Al Khalaileh, Abdel Rahman
    IEEE ACCESS, 2021, 9 (09): : 88512 - 88523
  • [29] Third-order exceptional points and frozen modes in planar elastic laminates
    Fishman, Ariel
    Elbaz, Guy
    Varma, T. Venkatesh
    Shmuel, Gal
    JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2024, 186
  • [30] Third-order nonlinearity by the inverse Faraday effect in planar magnetoplasmonic structures
    Im, Song-Jin
    Ri, Chol-Song
    Ho, Kum-Song
    Herrmann, Joachim
    PHYSICAL REVIEW B, 2017, 96 (16)
12345