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Title: Branch Structure Of J-Holomorphic Curves Near Periodic Orbits Of A Contact Manifold
Contributor(s): Harris, Adam  (author)orcid ; Wysocki, Krzysztof (author)
Publication Date: 2008
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Abstract: Let M be a three–dimensional contact manifold, and ψ : D \{0} → M x ℝ a finite–energy pseudoholomorphic map from the punctured disc in ℂ that is asymptotic to a periodic orbit of the contact form. This article examines conditions under which smooth coordinates may be defined in a tubular neighbourhood of the orbit such that ψ resembles a holomorphic curve, invoking comparison with the theory of topological linking of plane complex algebroid curves near a singular point. Examples of this behaviour, which are studied in some detail, include pseudoholomorphic maps into Ep,q x R, where Ep,q denotes a rational ellipsoid (contact structure induced by the standard complex structure on ℂ²), as well as contact structures arising from non-standard circle–fibrations of the three–sphere.
Publication Type: Journal Article
Source of Publication: American Mathematical Society Transactions, 360(4), p. 2131-2152
Publisher: American Mathematical Society
Place of Publication: Providence (RI), USA
ISSN: 0002-9947
Field of Research (FOR): 010111 Real and Complex Functions (incl Several Variables)
Socio-Economic Outcome Codes: 970101 Expanding Knowledge in the Mathematical Sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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