one-dimensional attractor

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• Attractor — For other uses, see Attractor (disambiguation). Visual representation of a strange attractor An attractor is a set towards which a dynamical system evolves over time. That is, points that get close enough to the attractor remain close even if… …   Wikipedia

• Chaos theory — This article is about chaos theory in Mathematics. For other uses of Chaos theory, see Chaos Theory (disambiguation). For other uses of Chaos, see Chaos (disambiguation). A plot of the Lorenz attractor for values r = 28, σ = 10, b = 8/3 …   Wikipedia

• Solenoid (mathematics) — This page discusses a class of topological groups. For the wrapped loop of wire, see Solenoid. The Smale Williams solenoid. In mathematics, a solenoid is a compact connected topological space (i.e. a continuum) that may be obtained as the inverse …   Wikipedia

• Fractal dimension — In fractal geometry, the fractal dimension, D , is a statistical quantity that gives an indication of how completely a fractal appears to fill space, as one zooms down to finer and finer scales. There are many specific definitions of fractal… …   Wikipedia

• Poincaré–Bendixson theorem — In mathematics, the Poincaré–Bendixson theorem is a statement about the long term behaviour of orbits of continuous dynamical systems on the plane. Overview The Poincaré–Bendixson theorem states that any orbit which stays in a compact region of… …   Wikipedia

• Autonomous system (mathematics) — In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not depend on the independent variable. Many laws in physics, where the independent variable is usually assumed to… …   Wikipedia

• Feigenbaum function — In the study of dynamical systems the term Feigenbaum function has been used to describe two different functions introduced by the physicist Mitchell Feigenbaum: * the solution to the Feigenbaum Cvitanović functional equation; and * the scaling… …   Wikipedia

• Saddle-node bifurcation — In the mathematical area of bifurcation theory a saddle node bifurcation or tangential bifurcation is a local bifurcation in which two fixed points (or equilibria) of a dynamical system collide and annihilate each other. The term saddle node… …   Wikipedia

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• Dynamical systems theory — is an area of applied mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical …   Wikipedia

• Smale's problems — refers to a list of eighteen unsolved problems in mathematics, proposed by Steve Smale in 2000. [Steve Smale, [http://www6.cityu.edu.hk/ma/people/smale/pap104.pdf Mathematical problems for the next century] . Mathematics: frontiers and… …   Wikipedia