Rotational chaos and strange attractors on the 2-torus
We construct a 2-torus homeomorphism h homotopic to the identity with an attracting R. H. Bing’s pseudocircle C such that the rotation set of h | C is not a unique vector. The only known examples of such an attractor were Birkhoff’s attractors, arising for dissipative maps with a twist. Our construc...
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| Veröffentlicht in: | Mathematische Zeitschrift 2015-04, Vol.279 (3-4), p.689-702 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We construct a 2-torus homeomorphism
h
homotopic to the identity with an attracting R. H. Bing’s pseudocircle
C
such that the rotation set of
h
|
C
is not a unique vector. The only known examples of such an attractor were Birkhoff’s attractors, arising for dissipative maps with a twist. Our construction relies heavily on the Barge–Martin method for constructing attractors as inverse limits of graphs. |
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| ISSN: | 0025-5874 1432-1823 |
| DOI: | 10.1007/s00209-014-1388-1 |