Centre families in two-dimensional complex holomorphic dynamical systems

被引：4

作者：

Needham, DJ ^{[1
]}

McAllister, S ^{[1
]}

机构：

[1] Univ Reading, Dept Math, Reading RG6 6AX, Berks, England

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 1998年 / 454卷 / 1976期

关键词：

dynamical systems; holomorphic; centre families;

D O I：

10.1098/rspa.1998.0258

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We consider a two-dimensional complex holomorphic dynamical system. In particular, we use the singular point theory of C. H. Briot and J. C. Bouquet to establish the existence of complex holomorphic invariant manifolds of the system in the neighbourhood of an equilibrium point with two purely imaginary eigenvalues. Consequently, this enables us to establish the existence of isochronous centre families in the neighbourhood of the equilibrium point. The results are exhibited by application to the complex Takens-Bogdanov system.

引用

页码：2267 / 2278

页数：12

共 50 条

[31] On Global Transversality and Chaos in Two-Dimensional Nonlinear Dynamical Systems
Luo, Albert C. J.
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, 2007, 2 (03): : 242 - 248
[32] Dynamical symmetries of two-dimensional systems in relativistic quantum mechanics
Zhang, Fu-Lin
Song, Ci
Chen, Jing-Ling
ANNALS OF PHYSICS, 2009, 324 (01) : 173 - 177
[33] Nonlinear dynamical symmetries of some two-dimensional quantum systems
Ruan, D
Sun, HZ
COMMUNICATIONS IN THEORETICAL PHYSICS, 2004, 42 (03) : 379 - 384
[34] Dynamical Properties of Two-Dimensional Aggregates in Patchy Particle Systems
Chrzanowska, A.
Kurzyk, J.
Karbowniczek, P.
NANOPLASMONICS, NANO-OPTICS, NANOCOMPOSITES, AND SURFACE STUDIES, 2015, 167 : 265 - 271
[35] Three-dimensional stratifications, knots and bifurcations of two-dimensional dynamical systems
Banks, SP
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2002, 12 (01): : 1 - 21
[36] Construction of exact complex dynamical invariant of a two-dimensional classical system
Fakir Chand
S C Mishra
Pramana, 2006, 67 : 999 - 1009
[37] Construction of exact complex dynamical invariant of a two-dimensional classical system
Chand, Fakir
Mishra, S. C.
PRAMANA-JOURNAL OF PHYSICS, 2006, 67 (06): : 999 - 1009
[38] Structural, dynamical and melting properties of two-dimensional clusters of complex plasmas
Kong, MH
Partoens, B
Peeters, FM
NEW JOURNAL OF PHYSICS, 2003, 5
[39] DYNAMICAL PROPERTIES OF FAMILIES OF HOLOMORPHIC MAPPINGS
Pal, Ratna
Verma, Kaushal
CONFORMAL GEOMETRY AND DYNAMICS, 2015, 19 : 323 - 350
[40] DYNAMICAL BEHAVIORS OF A DISCRETE TWO-DIMENSIONAL COMPETITIVE SYSTEM EXACTLY DRIVEN BY THE LARGE CENTRE
Du, Binbin
Wu, Changjian
Zhang, Guang
Zhou, Xiao-Liang
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2024, 14 (05): : 2822 - 2844

← 1 2 3 4 5 →