Add to ORKGA general geometric approach is given for bifurcation problems with homoclinic orbits to nonhyperbolic equilbrium points of ordinary differential equations. It consists of a special normal form called admissible variables, exponential expansion, strong A-lemma, and Lyapnunov- Schmidt reduction for the Poincare maps under Sil\u27nikov variables. The method is based on the Center Manifold Theory, the contraction mapping principle, and the Implicit Function Theorem
AbstractWe discuss numerical methods for the computation and continuation of equilibria and bifurcat...
AbstractConsider the equation ẍ − x + x2 = −λ1x + λ2ƒ(t) where ƒ(t + 1) = ƒ(t) and λ = (λ1, λ2) is ...
The bifurcation of the birth of a closed invariant curve in the two-parameter unfolding of a two-dim...
A general geometric approach is given for bifurcation problems with homoclinic orbits to nonhyperbol...
AbstractWe study bifurcations of homoclinic orbits to hyperbolic saddle equilibria in a class of fou...
AbstractIn this paper the bifurcation of a homoclinic orbit is studied for an ordinary differential ...
AbstractBy using Lyapunov–Schmidt reduction and exponential dichotomies, the persistence of homoclin...
AbstractNonautomonous ordinary differential equations, depending on two parameters μ1 and μ2, are co...
AbstractRegarding the small perturbation as a parameter in an appropriate space of functions, we can...
AbstractIn this paper we discuss a small nonautonomous perturbation of an autonomous system on Rn wh...
A procedure is derived which allows for a systematic construction of three-dimensional ordinary diff...
summary:The paper deals with the bifurcation phenomena of heteroclinic orbits for diffeomorphisms. T...
AbstractPerturbed discrete systems likexn+1=f(xn)+μg(xn,μ),xn∈RN,n∈Z, when the associated unperturbe...
In this article, center-manifold theory for homoclinic solutions of ordinary differential equations ...
AbstractDifferential equations are considered which contain a small parameter. When the parameter is...
AbstractWe discuss numerical methods for the computation and continuation of equilibria and bifurcat...
AbstractConsider the equation ẍ − x + x2 = −λ1x + λ2ƒ(t) where ƒ(t + 1) = ƒ(t) and λ = (λ1, λ2) is ...
The bifurcation of the birth of a closed invariant curve in the two-parameter unfolding of a two-dim...
A general geometric approach is given for bifurcation problems with homoclinic orbits to nonhyperbol...
AbstractWe study bifurcations of homoclinic orbits to hyperbolic saddle equilibria in a class of fou...
AbstractIn this paper the bifurcation of a homoclinic orbit is studied for an ordinary differential ...
AbstractBy using Lyapunov–Schmidt reduction and exponential dichotomies, the persistence of homoclin...
AbstractNonautomonous ordinary differential equations, depending on two parameters μ1 and μ2, are co...
AbstractRegarding the small perturbation as a parameter in an appropriate space of functions, we can...
AbstractIn this paper we discuss a small nonautonomous perturbation of an autonomous system on Rn wh...
A procedure is derived which allows for a systematic construction of three-dimensional ordinary diff...
summary:The paper deals with the bifurcation phenomena of heteroclinic orbits for diffeomorphisms. T...
AbstractPerturbed discrete systems likexn+1=f(xn)+μg(xn,μ),xn∈RN,n∈Z, when the associated unperturbe...
In this article, center-manifold theory for homoclinic solutions of ordinary differential equations ...
AbstractDifferential equations are considered which contain a small parameter. When the parameter is...
AbstractWe discuss numerical methods for the computation and continuation of equilibria and bifurcat...
AbstractConsider the equation ẍ − x + x2 = −λ1x + λ2ƒ(t) where ƒ(t + 1) = ƒ(t) and λ = (λ1, λ2) is ...
The bifurcation of the birth of a closed invariant curve in the two-parameter unfolding of a two-dim...