On the Singularity of the Conjugation Between Piecewise-Smooth Circle Homeomorphisms
Let f 1 and f 2 be two orientation-preserving circle homeomorphisms with the same irrational rotation number ρ and each with a single break point b 1 and b 2 , respectively. Suppose that the derivatives D f 1 and D f 2 satisfy a certain Zygmund condition except break points and the jumps σ ( b 1 ) =...
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| Veröffentlicht in: | Bulletin of the Malaysian Mathematical Sciences Society 2018-07, Vol.41 (3), p.1607-1622 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
f
1
and
f
2
be two orientation-preserving circle homeomorphisms with the same irrational rotation number
ρ
and each with a single break point
b
1
and
b
2
, respectively. Suppose that the derivatives
D
f
1
and
D
f
2
satisfy a certain Zygmund condition except break points and the jumps
σ
(
b
1
)
=
D
f
1
(
b
1
-
0
)
D
f
1
(
b
1
+
0
)
,
σ
(
b
2
)
=
D
f
2
(
b
2
-
0
)
D
f
1
(
b
2
+
0
)
do not coincide. Then the map
ψ
conjugating
f
1
and
f
2
is singular. |
|---|---|
| ISSN: | 0126-6705 2180-4206 |
| DOI: | 10.1007/s40840-017-0535-3 |