QUADRATIC MAPS WITHOUT ASYMPTOTIC MEASURE

被引:84
作者
HOFBAUER, F [1 ]
KELLER, G [1 ]
机构
[1] UNIV ERLANGEN NURNBERG,INST MATH,W-8520 ERLANGEN,GERMANY
关键词
D O I
10.1007/BF02096761
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
An interval map is said to have an asymptotic measure if the time averages of the iterates of Lebesgue measure converge weakly. We construct quadratic maps which have no asymptotic measure. We also find examples of quadratic maps which have an asymptotic measure with very unexpected properties, e.g. a map with the point mass on an unstable fix point as asymptotic measure. The key to our construction is a new characterization of kneading sequences. © 1990 Springer-Verlag.
引用
收藏
页码:319 / 337
页数:19
相关论文
共 24 条
[1]  
BENEDICKS M, 1983, ANN MATH, V122, P1
[2]  
BOWEN R, 1975, LECTURE NOTES MATH, V470
[3]  
Collet P., 1983, ERGOD THEOR DYN SYST, V3, P13
[4]  
DENKER M, 1976, LECT NOTES MATH, V527
[5]   SOFIC SYSTEMS AND GRAPHS [J].
FISCHER, R .
MONATSHEFTE FUR MATHEMATIK, 1975, 80 (03) :179-186
[6]   SENSITIVE DEPENDENCE TO INITIAL CONDITIONS FOR ONE DIMENSIONAL MAPS [J].
GUCKENHEIMER, J .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1979, 70 (02) :133-160
[8]   INTRINSIC ERGODICITY OF PIECEWISE MONOTONIC TRANSFORMATIONS WITH POSITIVE ENTROPY [J].
HOFBAUER, F .
ISRAEL JOURNAL OF MATHEMATICS, 1979, 34 (03) :213-237
[9]   THE TOPOLOGICAL ENTROPY OF THE TRANSFORMATION X-]AX(1-X) [J].
HOFBAUER, F .
MONATSHEFTE FUR MATHEMATIK, 1980, 90 (02) :117-141
[10]  
HOFBAUER F, 1982, ERGODIC THEORY RELAT, P85