Bifurcation of homoclinics
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Publication:5429431
DOI10.1090/S0002-9939-07-09088-0zbMath1134.34023OpenAlexW1976987879MaRDI QIDQ5429431
Publication date: 30 November 2007
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0002-9939-07-09088-0
Bifurcation theory for ordinary differential equations (34C23) (Semi-) Fredholm operators; index theories (47A53) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Boundary value problems on infinite intervals for ordinary differential equations (34B40) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)
Related Items
Maslov index for heteroclinic orbits of non-Hamiltonian systems on a two-dimensional phase space ⋮ Bifurcation of heteroclinic orbits via an index theory ⋮ Spectral flow, crossing forms and homoclinics of Hamiltonian systems ⋮ The index bundle for selfadjoint Fredholm operators and multiparameter bifurcation for Hamiltonian systems ⋮ Fredholm theory of families of discrete dynamical systems and its applications to bifurcation theory ⋮ Global bifurcation of homoclinic trajectories of discrete dynamical systems ⋮ Bifurcation of homoclinics of Hamiltonian systems ⋮ The family index theorem and bifurcation of solutions of nonlinear elliptic BVP ⋮ The index bundle and multiparameter bifurcation for discrete dynamical systems
Cites Work
- The splitting index for linear differential systems
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- Dichotomies in stability theory
- Degree theory for \(C^1\) Fredholm mappings of index 0
- Global bifurcation of homoclinic solutions of Hamiltonian systems
- Ordinary differential operators in Hilbert spaces and Fredholm pairs
- The Conley index over the circle
- Bifurcation from simple eigenvalues
- Exponential Dichotomies and Fredholm Operators
- Parity and Generalized Multiplicity
