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Symmetry, Integrability and Geometry: Methods and Applications, 2018, Volume 14, 084, 66 pp.
DOI: https://doi.org/10.3842/SIGMA.2018.084 (Mi sigma1383) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Faithful Semitoric Systems

Sonja Hohlocha, Silvia Sabatinib, Daniele Sepec, Margaret Symingtond

a Department of Mathematics - Computer Science, University of Antwerpen, Campus Middelheim, Building G, M.G.211, Middelheimlaan 1, 2020 Antwerpen, Belgium
b Mathematisches Institut, Universität zu Köln, Weyertal 86-90, D-50931 Köln, Germany
c Universidade Federal Fluminense, Instituto de Matemática, Departamento de Matemática Aplicada, Rua Professor Marcos Waldemar de Freitas Reis, s/n, Bloco H, Campus do Gragoatá, CEP 24210-201, Niterói, RJ, Brazil
d Department of Mathematics, Mercer University, 1501 Mercer University Drive, Macon, GA 31207, USA
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DOI: https://doi.org/10.3842/SIGMA.2018.084
Abstract: This paper consists of two parts. The first provides a review of the basic properties of integrable and almost-toric systems, with a particular emphasis on the integral affine structure associated to an integrable system. The second part introduces faithful semitoric systems, a generalization of semitoric systems (introduced by Vũ Ngọc and classified by Pelayo and Vũ Ngọc) that provides the language to develop surgeries on almost-toric systems in dimension 4. We prove that faithful semitoric systems are natural building blocks of almost-toric systems. Moreover, we show that they enjoy many of the properties that their (proper) semitoric counterparts do.
Keywords: completely integrable Hamiltonian systems; almost toric systems; semitoric systems; integral affine geometry; focus-focus singularities.
Funding agency Grant number
Deutsche Forschungsgemeinschaft SFB-TRR 191
Netherlands Organization for Scientific Research 639.031.345
National Council for Scientific and Technological Development (CNPq) 409552/2016-0
S.H. was partially supported by the Research Fund of the University of Antwerp and by SwissMAP. S.S. was partially supported by SFB-TRR 191 Symplectic Structures in Geometry, Algebra and Dynamics, funded by the Deutsche Forschungsgemeinschaft. D.S. was partially supported by the University of Cologne, SwissMAP, the NWO Veni grant 639.031.345 and by the CNPq Universal grant 409552/2016-0. M.S. was partially supported by Mercer University, the Institute of Pure and Applied Mathematics (IMPA) in Rio de Janeiro, the University of Cologne, and the Swiss Federal Institute of Technology (ETH) in Zurich.
Received: July 7, 2017; in final form July 30, 2018; Published online August 16, 2018
Bibliographic databases:
Document Type: Article
MSC: 37J35; 37J05; 53D20; 70H06
Language: English
Citation: Sonja Hohloch, Silvia Sabatini, Daniele Sepe, Margaret Symington, “Faithful Semitoric Systems”, SIGMA, 14 (2018), 084, 66 pp.
Citation in format AMSBIB
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