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Title: | Periodic Center Manifolds for Nonhyperbolic Limit Cycles in ODEs | Authors: | LENTJES, Bram Windmolders, Mattias Kuznetsov, Yuri A. |
Issue Date: | 2023 | Publisher: | WORLD SCIENTIFIC PUBL CO PTE LTD | Source: | INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 33 (15) (Art N° 2350184) | Abstract: | In this paper, we deal with a classical object, namely, a nonhyperbolic limit cycle in a system of smooth autonomous ordinary differential equations. While the existence of a center manifold near such a cycle was assumed in several studies on cycle bifurcations based on periodic normal forms, no proofs were available in the literature until recently. The main goal of this paper is to give an elementary proof of the existence of a periodic smooth locally invariant center manifold near a nonhyperbolic cycle in finite-dimensional ordinary differential equations by using the Lyapunov–Perron method. In addition, we provide several explicit examples of analytic vector fields admitting (non)-unique, (non)-$C^{\infty}$-smooth and (non)-analytic periodic center manifolds. | Notes: | Lentjes, B (corresponding author), Hasselt Univ, Dept Math, B-3590 Diepenbeek, Belgium. bram.lentjes@uhasselt.be; mattias.windmolders@student.kuleuven.be; i.a.kouznetsov@uu.nl |
Keywords: | Center manifold theorem;nonhyperbolic cycle;ordinary differential equation | Document URI: | http://hdl.handle.net/1942/42031 | ISSN: | 0218-1274 | e-ISSN: | 1793-6551 | DOI: | 10.1142/S0218127423501845 | ISI #: | 001123635100002 | Category: | A1 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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Periodic Center Manifolds for Nonhyperbolic Limit Cycles in ODEs.pdf | Peer-reviewed author version | 18.73 MB | Adobe PDF | View/Open |
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