Piecewise isometries have zero topological entropy

被引：0

作者：

Buzzi, J ^{[1
]}

机构：

[1] Ecole Polytech, Ctr Math, CNRS, UMR 7640, F-91128 Palaiseau, France

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2001年 / 21卷

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D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that piecewise isometries, i.e. non-necessarily invertible maps defined on a finite union of polytopes and coinciding with an isometry on the interior of each polytope, have zero topological entropy in any dimension. This had been conjectured by a number of authors. The proof is by an induction on the dimension and uses a device (the differential of a piecewise linear map) introduced by M. Tsujii.

引用

页码：1371 / 1377

页数：7

共 7 条

[1] Intrinsic ergodicity of affine maps in [0, 1](d) [J].

Buzzi, J .

MONATSHEFTE FUR MATHEMATIK, 1997, 124 (02) :97-118

[2]

Denker M., 1976, LECT NOTES MATH, V527

[3] Sofic subshifts and piecewise isometric systems [J].

Goetz, A .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1999, 19 :1485-1501

[4] Topological entropy of polygon exchange transformations and polygonal billiards [J].

Gutkin, E ;

Haydn, N .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1997, 17 :849-867

[5] THE GROWTH-RATE FOR THE NUMBER OF SINGULAR AND PERIODIC-ORBITS FOR A POLYGONAL BILLIARD [J].

KATOK, A .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1987, 111 (01) :151-160

[6]

KELLER G, 1979, CR ACAD SCI A MATH, V289, P625

[7]

TSUJII M, IN PRESS MATH INVENT

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