From homoclinics to quasi-periodic solutions for ordinary differential equations. Issue 5 (1st September 2015)

• Record Type: Journal Article
• Authors: Zhu, Changrong
• Is Part Of: Proceedings. Volume 145:Issue 5(2015)
• Page Start: 1091
• Page End: 1114
• Publication Date: 2015-09-01
• Subjects: degenerate homoclinic solution, -- quasi-periodic solution, -- Lyapunov–Schmidt reduction, -- Fredholm alternative, -- exponential dichotomy; Primary 35K65, -- 35K70; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210515000189
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : We consider the quasi-periodic solutions bifurcated from a degenerate homoclinic solution. Assume that the unperturbed system has a homoclinic solution and a hyperbolic fixed point. The bifurcation function for the existence of a quasi-periodic solution of the perturbed system is obtained by functional analysis methods. The zeros of the bifurcation function correspond to the existence of the quasi-periodic solution at the non-zero parameter values. Some solvable conditions of the bifurcation equations are investigated. Two examples are given to illustrate the results.