SENSITIVE DEPENDENCE TO INITIAL CONDITIONS FOR ONE DIMENSIONAL MAPS

被引：317

作者：

GUCKENHEIMER, J

机构：

[1] Department of Mathematics, University of California, Santa Cruz, 95060, CA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1979年 / 70卷 / 02期

关键词：

D O I：

10.1007/BF01982351

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper studies the iteration of maps of the interval which have negative Schwarzian derivative and one critical point. The maps in this class are classified up to topological equivalence. The equivalence classes of maps which display sensitivity to initial conditions for large sets of initial conditions are characterized. © 1979 Springer-Verlag.

引用

页码：133 / 160

页数：28

共 29 条

[1] HYPERGRAPHIC FUNCTIONS AND BIFURCATIONS IN RECURRENCE RELATIONS
ALLWRIGHT, DJ
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 1978, 34 (04) : 687 - 691
[2] EXISTENCE OF PERIODIC POINTS FOR MAPS OF S-1
BLOCK, L
FRANKE, J
[J]. INVENTIONES MATHEMATICAE, 1973, 22 (01) : 69 - 73
[3] BOWEN R, 1978, INVARIANT MEASURES M
[4] Cartan E., 1937, LECONS THEORIE ESPAC
[5] Denjoy A., 1932, J MATH PURE APPL, V11, P333
[6] BIFURCATION OF MAPS OF INTERVAL
GUCKENHEIMER, J
[J]. INVENTIONES MATHEMATICAE, 1977, 39 (02) : 165 - 178
[7] DYNAMICS OF DENSITY DEPENDENT POPULATION MODELS
GUCKENHEIMER, J
OSTER, G
IPAKTCHI, A
[J]. JOURNAL OF MATHEMATICAL BIOLOGY, 1977, 4 (02) : 101 - 147
[8] GUCKENHEIMER J, 1978, BIFURCATIONS DYNAMIC
[9] 2-DIMENSIONAL MAPPING WITH A STRANGE ATTRACTOR
HENON, M
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1976, 50 (01) : 69 - 77
[10] HERMAN M, 1976, THESIS ORSAY

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