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Publication . Article . Preprint . 2021

On Limit Sets for Geodesics of Meromorphic Connections

Novikov, Dmitry; Shapiro, Boris; Tahar, Guillaume;
Open Access
Published: 24 Dec 2021 Journal: Journal of Dynamical and Control Systems (issn: 1079-2724, eissn: 1573-8698, Copyright policy )
Publisher: Springer Science and Business Media LLC
Meromorphic connections on Riemann surfaces originate and are closely related to the classical theory of linear ordinary differential equations with meromorphic coefficients. Limiting behaviour of geodesics of such connections has been studied by e.g. Abate, Bianchi and Tovena in relation with generalized Poincar\'{e}-Bendixson theorems. At present, it seems still to be unknown whether some of the theoretically possible asymptotic behaviours of such geodesics really exist. In order to fill the gap, we use the branched affine structure induced by a Fuchsian meromorphic connection to present several examples with geodesics having infinitely many self-intersections and quite peculiar omega-limit sets.
Comment: 15 pages, 4 figures

Control and Optimization, Numerical Analysis, Algebra and Number Theory, Control and Systems Engineering, Dynamical Systems (math.DS), Differential Geometry (math.DG), FOS: Mathematics, [2010] Primary 37F75, Secondary 32S65, Mathematics - Dynamical Systems, Mathematics - Differential Geometry

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12 references, page 1 of 2

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Funded by
EC| EffectiveTG
Effective Methods in Tame Geometry and Applications in Arithmetic and Dynamics
  • Funder: European Commission (EC)
  • Project Code: 802107
  • Funding stream: H2020 | ERC | ERC-STG