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Existence of orbits with non-zero torsion for certain types of surface diffeomorphisms
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- Béguin François
- Laboratoire d'Analyse, Géométrie et Applications, Université Paris Nord
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- Boubaker Zouhour Rezig
- Universit du 7 Novembre à Carthage, Faculté des Sciences de Bizerte, Département de Mathématiques
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Description
The present paper concerns the dynamics of surface diffeomorphisms. Given a diffeomorphism f of a surface S, the torsion of the orbit of a point z ∈ S is, roughly speaking, the average speed of rotation of the tangent vectors under the action of the derivative of f, along the orbit of z under f. The purpose of the paper is to identify some situations where there exist measures and orbits with non-zero torsion. We prove that every area preserving diffeomorphism of the disc which coincides with the identity near the boundary has an orbit with non-zero torsion. We also prove that a diffeomorphism of the torus ${\mathbb T}^2$, isotopic to the identity, whose rotation set has non-empty interior, has an orbit with non-zero torsion.
Journal
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 65 (1), 137-168, 2013
The Mathematical Society of Japan
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Details 詳細情報について
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- CRID
- 1390282680091772032
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- NII Article ID
- 10031177276
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- NII Book ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- NDL BIB ID
- 024209012
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- Text Lang
- en
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- Data Source
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- JaLC
- NDL Search
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed