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The Maslov Index and Global Bifurcation for Nonlinear Boundary Value Problems

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Stability and Bifurcation Theory for Non-Autonomous Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2065))

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Abstract

We first describe the notion of Maslov index and relate it to the concepts of moment of verticality and of phase-angles. We then illustrate the role of the Maslov index in the development of global bifurcation results for nonlinear first order differential systems in \({\mathbb{R}}^{2N}\) and for nonlinear planar Dirac-type systems.

Lectures given by the second author at the C.I.M.E. course “Stability and Bifurcation for nonautonomous differential equations”, Cetraro, Italy, June 20–June 25, 2011.

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Notes

  1. 1.

    Lectures given by the second author at the C.I.M.E. course “Stability and Bifurcation for non-autonomous differential equations”, Cetraro, Italy, June 20–June 25, 2011.

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Acknowledgements

We wish to thank J. Pejsachowicz for introducing us to the study of the Maslov index and for many fruitful conversations. The second author wishes to thank the C.I.M.E. foundation and the course directors R. Johnson and M.P. Pera for the kind invitation to deliver these lectures.

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Authors and Affiliations

  1. SISSA, International School for Advanced Studies, Via Bonomea 265, 34136, Trieste, Italy

    Alberto Boscaggin

  2. Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino, Italy

    Anna Capietto & Walter Dambrosio

Authors
  1. Alberto Boscaggin
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  2. Anna Capietto
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  3. Walter Dambrosio
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Correspondence to Anna Capietto .

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Boscaggin, A., Capietto, A., Dambrosio, W. (2013). The Maslov Index and Global Bifurcation for Nonlinear Boundary Value Problems. In: Stability and Bifurcation Theory for Non-Autonomous Differential Equations. Lecture Notes in Mathematics(), vol 2065. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32906-7_1

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