AbstractA description of the principal bifurcations which lead to the appearance of the Lorenz attractor is given for the 3D normal form for codimension-3 bifurcations of equilibria and periodic orbits in systems with symmetry. We pay special attention to two bifurcation points corresponding to the formation of a homoclinic butterfly of a saddle with unit saddle index and to a homoclinic butterfly with zero separatrix value
AbstractConsider the equation ẍ − x + x2 = −λ1x + λ2ƒ(t) where ƒ(t + 1) = ƒ(t) and λ = (λ1, λ2) is ...
A procedure is derived which allows for a systematic construction of three-dimensional ordinary diff...
In this work we investigate the dynamical behavior of two dynamical systems: (i) a symmetric linear ...
AbstractA description of the principal bifurcations which lead to the appearance of the Lorenz attra...
Lorenz-like attractors are known to appear in unfoldings from certain codimension two homoclinic bif...
We present a case study elaborating on the multiplicity and self-similarity of homoclinic and hetero...
We study dynamics and bifurcations of three-dimensional diffeomorphisms with nontransversal heterocl...
In this paper we consider the interaction of the Lorenz manifold - the two-dimensional stable manifo...
In this paper we study the local codimension one and two bifurcations which occur in a family of thr...
The homoclinic bifurcation properties of a planar dynamical system are analyzed and the correspondin...
We give an analytic (free of computer assistance) proof of the existence of a classical Lorenz attra...
We explore the multifractal, self-similar organization of heteroclinic and homoclinic bifurcations o...
In this paper, we suggest some sufficient conditions for the existence of homoclinic orbits of the o...
We consider certain kinds of homoclinic bifurcations in three-dimensional vector fields. These globa...
An overview of homoclinic and heteroclinic bifurcation theory for autonomous vector fields is given....
AbstractConsider the equation ẍ − x + x2 = −λ1x + λ2ƒ(t) where ƒ(t + 1) = ƒ(t) and λ = (λ1, λ2) is ...
A procedure is derived which allows for a systematic construction of three-dimensional ordinary diff...
In this work we investigate the dynamical behavior of two dynamical systems: (i) a symmetric linear ...
AbstractA description of the principal bifurcations which lead to the appearance of the Lorenz attra...
Lorenz-like attractors are known to appear in unfoldings from certain codimension two homoclinic bif...
We present a case study elaborating on the multiplicity and self-similarity of homoclinic and hetero...
We study dynamics and bifurcations of three-dimensional diffeomorphisms with nontransversal heterocl...
In this paper we consider the interaction of the Lorenz manifold - the two-dimensional stable manifo...
In this paper we study the local codimension one and two bifurcations which occur in a family of thr...
The homoclinic bifurcation properties of a planar dynamical system are analyzed and the correspondin...
We give an analytic (free of computer assistance) proof of the existence of a classical Lorenz attra...
We explore the multifractal, self-similar organization of heteroclinic and homoclinic bifurcations o...
In this paper, we suggest some sufficient conditions for the existence of homoclinic orbits of the o...
We consider certain kinds of homoclinic bifurcations in three-dimensional vector fields. These globa...
An overview of homoclinic and heteroclinic bifurcation theory for autonomous vector fields is given....
AbstractConsider the equation ẍ − x + x2 = −λ1x + λ2ƒ(t) where ƒ(t + 1) = ƒ(t) and λ = (λ1, λ2) is ...
A procedure is derived which allows for a systematic construction of three-dimensional ordinary diff...
In this work we investigate the dynamical behavior of two dynamical systems: (i) a symmetric linear ...
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