Towards a global view of dynamical systems, for the C1-topology

被引:37
作者
Bonatti, C. [1 ]
机构
[1] Univ Bourgogne, Inst Math Bourgogne, CNRS, UMR 5584, F-21004 Dijon, France
关键词
PARTIALLY HYPERBOLIC SYSTEMS; HOMOCLINIC TANGENCIES; CENTRAL DIRECTION; SRB MEASURES; DIFFEOMORPHISMS; ATTRACTORS; STABILITY; RECURRENCE; SETS;
D O I
10.1017/S0143385710000891
中图分类号
O29 [应用数学];
学科分类号
070104 [应用数学];
摘要
This paper suggests a program for getting a global view of the dynamics of diffeomorphisms, from the point of view of the C-1-topology. More precisely, given any compact manifold M, one splits Diff(1) (M) into disjoint C-1-open regions whose union is C-1-dense, and conjectures state that each of these open sets and their complements is characterized by the presence of: either a robust local phenomenon; or a global structure forbidding this local phenomenon. Other conjectures state that some of these regions are empty. This set of conjectures draws a global view of the dynamics, putting in evidence the coherence of the numerous recent results on C-1-generic dynamics.
引用
收藏
页码:959 / 993
页数:35
相关论文
共 76 条
[1]
Generic diffeomorphisms on compact surfaces [J].
Abdenur, F ;
Bonatti, C ;
Crovisier, S ;
Díaz, LJ .
FUNDAMENTA MATHEMATICAE, 2005, 187 (02) :127-159
[2]
Generic robustness of spectral decompositions [J].
Abdenur, F .
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2003, 36 (02) :213-224
[3]
Abdenur F., ISRAEL J MA IN PRESS
[4]
ABRAHAM R, 1968, P S PURE MATH, V14
[5]
SRB measures for partially hyperbolic systems whose central direction is mostly expanding [J].
Alves, JF ;
Bonatti, C ;
Viana, M .
INVENTIONES MATHEMATICAE, 2000, 140 (02) :351-398
[6]
[Anonymous], 1970, Global analysis
[7]
[Anonymous], 1987, Pitman Res. Notes Math. Ser.
[8]
[Anonymous], ARXIV10112935
[9]
[Anonymous], MEM AM MATH SOC
[10]
[Anonymous], 1978, Isolated invariant sets and the Morse index