Links and bifurcations in nonsingular Morse-Smale systems

被引：0

作者：

Campos, B

Alfaro, JM

Vindel, P

机构：

[1] Univ Jaume 1, Dept Matemat, E-12071 Castello, Spain

[2] Univ Valencia, Fac Matemat, Dept Matemat Aplicada, Burjassot, Valencia, Spain

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 1997年 / 7卷 / 08期

关键词：

D O I：

10.1142/S0218127497001345

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Wada's theorem classifies the set of periodic orbits in NMS systems on S-3 as links, that can be written in terms of six operations. This characterization allows us to study the topological restrictions that links require to suffer a given codimension one bifurcation. Moreover, these results are reproduced in the case of NMS systems with rotational symmetries, introducing new geometrical tools.

引用

页码：1717 / 1736

页数：20

共 50 条

[1] LINKS OF CLOSED ORBITS OF NONSINGULAR MORSE-SMALE FLOWS
SASANO, K
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (04) : 727 - 734
[2] Bifurcations of links of periodic orbits in non-singular Morse-Smale systems on S-3
Campos, B
Alfaro, JM
Vindel, P
[J]. NONLINEARITY, 1997, 10 (05) : 1339 - 1355
[3] Bifurcations of Morse-Smale diffeomorphisms with wildly embedded separatrices
Bonatti C.
Grines V.Z.
Medvedev V.S.
Pochinka O.V.
[J]. Proceedings of the Steklov Institute of Mathematics, 2007, 256 (1) : 47 - 61
[4] From Morse-Smale to all knots and links
Ghrist, R
Young, T
[J]. NONLINEARITY, 1998, 11 (04) : 1111 - 1125
[5] MORSE-SMALE SYSTEMS AND THE HOMOLOGY THEORY
FELSHTYN, AL
[J]. IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENII MATEMATIKA, 1982, (09): : 58 - 66
[6] Global dynamics of Morse-Smale systems
E. V. Zhuzhoma
V. S. Medvedev
[J]. Proceedings of the Steklov Institute of Mathematics, 2008, 261
[7] Bifurcations of links of periodic orbits in non-singular Morse-Smale systems with a rotational symmetry on S3
Campos, B
Alfaro, JM
Vindel, P
[J]. TOPOLOGY AND ITS APPLICATIONS, 2000, 102 (03) : 279 - 295
[8] Global Dynamics of Morse-Smale Systems
Zhuzhoma, E. V.
Medvedev, V. S.
[J]. PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2008, 261 (01) : 112 - 135
[9] Critical saddle-node bifurcations and Morse-Smale maps
Hunt, BR
Young, TR
[J]. PHYSICA D-NONLINEAR PHENOMENA, 2004, 197 (1-2) : 1 - 17
[10] ON MORSE-SMALE DIFFEOMORPHISMS
PALIS, J
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1968, 74 (05) : 985 - &

← 1 2 3 4 5 →