Constru tion of urious minimal uniquely ergodi
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ar X iv :m at h. D S/ 06 05 43 8 v1 16 M ay 2 00 6 Constru tion of urious minimal uniquely ergodi homeomorphisms on manifolds: the Denjoy-Rees te hnique F. Beguin y , S. Crovisier z and F. Le Roux x 17th May 2006 Abstra t In [23?, Mary Rees has onstru ted a minimal homeomorphism of the 2-torus with pos- itive topologi al entropy. This homeomorphism f is obtained by enri hing the dynami s of an irrational rotation R. We improve Rees onstru tion, allowing to start with any homeomorphism R instead of an irrational rotation and to ontrol pre isely the measurable dynami s of f . This yields in parti ular the following result: Any ompa t manifold of dimension d 2 whi h arries a minimal uniquely ergodi homeomorphism also arries a minimal uniquely ergodi homeomorphism with positive topologi al entropy. More generally, given some homeomorphism R of a ( ompa t) manifold and some home- omorphism h C of a Cantor set, we onstru t a homeomorphism f whi h \looks like R from the topologi al viewpoint and \looks like R h C from the measurable viewpoint.
- topologi al
- ergodi homeomorphisms
- minimal homeomorphism
- minimal uniquely
- constru tion
- ting examples
- stri tly
- tion pro
- measurable dynami
oratoire
i
lik
Construction
generally
of
a
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uniquely
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homeomorphisms
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on
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manifolds:
the
oin
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realisabilit
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hnique
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ematiques,
Ma
Cedex,
y
Analyse,
2006
Univ.
x
In
P
[23
rance.
℄
opy.
Mary
giv
Rees
R
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omorphism
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rance.
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et
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irrational
ematiques,
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.
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e
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37E30,
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ositive
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arXiv:math.DS/0605438 v1 16 May 2006.
Con
6.2
ten
.
ts
.
1
5
In
the
tro
.
.
1
of
1.1
.
Denjo
B
y-Rees
32
.
hnique
n
.
.
.
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en
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as
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1
.
;
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2
25
;
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3
sets
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.
26
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The
.
tor
.
K
.
C
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5
Construction
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of
.
the
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.
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set
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:
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realisation
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of
.
h
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otheses
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A
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1
.
;
.
2
.
;
27
3
Consequences
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h
.
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.
5
.
6
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.
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of
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20
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of
The
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of
;
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(
;
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;
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1
28
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6.1
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of
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and
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(
.
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32
.
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20
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;
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2
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3
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33
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othesis
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of
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desired
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in
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bres
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20
sc
3.3
35
Main
The
(
of
k
h
k
yp
1
otheses
(
B
k
1
k
;
1
2
.
;
.
3
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7.2
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.
1
.
2
.
3
.
