Global bifurcation of fixed points and the Poincaré translation operator on manifolds

DOI10.1007/BF01783474zbMath0944.37024MaRDI QIDQ1817941

Massimo Furi, Maria Patrizia Pera

Publication date: 4 January 2000

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

zbMATH Keywords

fixed pointsbifurcationdegree theoryperiodic ordinary differential equations

Mathematics Subject Classification ID

Bifurcations of singular points in dynamical systems (37G10) Flows on surfaces (37E35)

Related Items (5)

Periodic solutions of nonlinear hyperbolic evolution systems ⋮ Periodic solutions for nonlinear evolution equations at resonance ⋮ Global bifurcation results for nonlinear dynamic equations on time scales ⋮ Krasnosel'skii type formula and translation along trajectories method on the scale of fractional spaces ⋮ Topological degree methods for perturbations of operators generating compact \(C_0\) semigroups

Cites Work

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• A continuation principle for periodic solutions of forced motion equations on manifolds and applications to bifurcation theory
• A continuation principle for forced oscillations on differentiable manifolds
• The Euler characteristic of vector fields on Banach manifolds and a globalization of Leray-Schauder degree
• A global index for bifurcation of fixed points.
• Differential Topology
• The Operator of Translation Along the Trajectories of Differential Equations
• The Leray-Schauder index and the fixed point theory for arbitrary ANRs

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