Contact topology and hydrodynamics III: Knotted orbits

被引:35
作者
Etnyre, J [1 ]
Ghrist, R
机构
[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA
[2] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA
关键词
tight contact structures; Reeb flows; Euler equations; knots; templates;
D O I
10.1090/S0002-9947-00-02651-9
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We employ the relationship between contact structures and Beltrami fields derived in part I of this series to construct a steady nonsingular solution to the Euler equations on a Riemannian S-3 whose flowlines trace out closed curves of all possible knot and link types. Using careful contact-topological controls, we can make such vector fields real-analytic and transverse to the tight contact structure on S-3. Sufficient review of concepts is included to make this paper independent of the previous works in this series.
引用
收藏
页码:5781 / 5794
页数:14
相关论文
共 32 条
[1]  
AEBISCHER B, 1994, PROGR MATH, V124
[2]  
Arnold V. I., 1998, TOPOLOGICAL METHODS
[3]  
BENNEQUIN D, 1983, ASTERISQUE, P87
[4]  
Birman J., 1983, Contemp. Math., V20, P1, DOI DOI 10.1090/CONM/020/718132
[5]   KNOTTED PERIODIC-ORBITS IN DYNAMICAL-SYSTEMS .1. LORENZ EQUATIONS [J].
BIRMAN, JS ;
WILLIAMS, RF .
TOPOLOGY, 1983, 22 (01) :47-82
[6]   An ode whose solutions contain all knots and links [J].
Christ, RW ;
Holmes, PJ .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1996, 6 (05) :779-800
[7]   Gluing tight contact manifolds [J].
Colin, V .
BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1999, 127 (01) :43-69
[8]   CHAOTIC STREAMLINES IN THE ABC FLOWS [J].
DOMBRE, T ;
FRISCH, U ;
GREENE, JM ;
HENON, M ;
MEHR, A ;
SOWARD, AM .
JOURNAL OF FLUID MECHANICS, 1986, 167 :353-391
[9]   CONTACT 3-MANIFOLDS 20 YEARS SINCE MARTINET,J. WORK [J].
ELIASHBERG, Y .
ANNALES DE L INSTITUT FOURIER, 1992, 42 (1-2) :165-192
[10]   CLASSIFICATION OF OVERTWISTED CONTACT STRUCTURES ON 3-MANIFOLDS [J].
ELIASHBERG, Y .
INVENTIONES MATHEMATICAE, 1989, 98 (03) :623-637