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Homoclinic and heteroclinic bifurcations in vector fields. (English) Zbl 1243.37024
Broer, Henk (ed.) et al., Handbook of dynamical systems. Volume 3. Amsterdam: Elsevier (ISBN 978-0-444-53141-4/hbk; 978-0-444-63821-2/pbk; 978-0-08-093226-2/ebook). 379-524 (2010).
The goal of this paper is to review the existing literature on homoclinic and heteroclinic bifurcation theory for flows. More specifically, the authors focus on bifurcations from homoclinic and heteroclinic orbits between equilibria in autonomous ordinary differential equations \(\dot{u}=f(u,\mu)\), where \((u,\mu)\in\mathbb{R}^{n}\times\mathbb{R}^{m}\) and \(t\in\mathbb{R}\).
For the entire collection see [Zbl 1216.37002].

MSC:
37C27 Periodic orbits of vector fields and flows
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
37C29 Homoclinic and heteroclinic orbits for dynamical systems
37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations
Software:
HomCont; AUTO
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