homoclinic point

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• Homoclinic orbit — In mathematics, a homoclinic orbit is a trajectory of a flow of a dynamical system which joins a saddle equilibrium point to itself. More precisely, a homoclinic orbit lies in the intersection of the stable manifold and the unstable manifold of… …   Wikipedia

• Homoclinic bifurcation — In mathematics, a homoclinic bifurcation is a global bifurcation which often occurs when a periodic orbit collides with a saddle point.The image below shows a phase portrait before, at, and after a homoclinic bifurcation in 2D. The periodic orbit …   Wikipedia

• homoclinic — adjective Describing a path that starts and ends at the same point of equilibrium …   Wiktionary

• Horseshoe map — In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. It is a core example in the study of dynamical systems. The map was introduced by Smale while studying the behavior of the… …   Wikipedia

• Numerical continuation — is a method of computing approximate solutions of a system of parameterized nonlinear equations, The parameter λ is usually a real scalar, and the solution an n vector. For a fixed parameter value λ,, maps Euclidean n space into itself. Often the …   Wikipedia

• List of mathematics articles (H) — NOTOC H H cobordism H derivative H index H infinity methods in control theory H relation H space H theorem H tree Haag s theorem Haagerup property Haaland equation Haar measure Haar wavelet Haboush s theorem Hackenbush Hadamard code Hadamard… …   Wikipedia

• Heteroclinic orbit — In mathematics, in the phase portrait of a dynamical system, a heteroclinic orbit (sometimes called a heteroclinic connection) is a path in phase space which joins two different equilibrium points. If the equilibrium points at the start and end… …   Wikipedia

• Bifurcation theory — is the mathematical study of changes in the qualitative or topological structure of a given family. Examples of such families are the integral curves of a family of vector fields or, the solutions of a family of differential equations. Most… …   Wikipedia

• Markov partition — A Markov partition is a tool used in dynamical systems theory, allowing the methods of symbolic dynamics to be applied to the study of hyperbolic systems. By using a Markov partition, the system can be made to resemble a discrete time Markov… …   Wikipedia

• Lyapunov stability — In mathematics, the notion of Lyapunov stability occurs in the study of dynamical systems. In simple terms, if all solutions of the dynamical system that start out near an equilibrium point x e stay near x e forever, then x e is Lyapunov stable.… …   Wikipedia

• Infinite-period bifurcation — In mathematics, an infinite period bifurcation is a global bifurcation that can occur when two fixed points emerge on a limit cycle. As the limit of a parameter approaches a certain critical value, the speed of the oscillation slows down and the… …   Wikipedia