stable manifold

(redirected from Unstable manifold)

stable manifold

A mathematical term for the set of all points in phase space which are attracted to a fixed point or other invariant orbit in positive time.
References in periodicals archive ?
This also tells us the unstable manifold of the origin is one-dimensional.
represent the dimensions of the unstable manifold of P and that of the unstable and center manifolds of the origin.
According to [4] and [12], the tangent spaces of the corresponding stable and unstable manifolds should span the whole space and the intersection of such manifolds should be transversal.
b]], [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] a closure of the unstable manifold of [[LAMBDA].
for all natural j , the unstable manifold of F at [S.
0]-image, one can easily verify that the given set is a semi-locally unstable manifold [W.
Denote by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] the globally unstable manifold of [Y.
The circular area continuously deforms along the (perturbed) unstable manifold and tangles when it approaches to the (perturbed) hyperbolic fixed point.
8b) is obtained from the unstable manifold using the symmetry relation of the Poincare map (Eq 24).
Since the two manifolds are invariant and the Poincare map preserves orientation, the enclosed region should be mapped another enclosed region infinitely many times along the unstable manifold, as t(or z) [right arrow] [infinity], or, along the stable manifold, as t (or z] [right arrow] [infinity].
Eight papers cover filter banks and frames in the discrete periodic case; Newton polyhedra, asymptotics of volumes, and asymptotics of exponential integrals; approximation methods for unstable manifolds of equilibrium points of autonomous systems; the Steklov problems in symmetric domains with infinitely extended boundary; the spectrum of Steklov problems in peak-shaped domains; generalization of the Cwikel estimate for integral operators; asymptotic behavior of probabilities of moderate deviations; and the history of the study of convex polyhedra with regular faces and faces composed of regular ones.
In this new treatment of one of the most dynamic but difficult topics in modern theory, Chernov and Markarian keep the beginner in mind as they start from the basics and work through all the definitions and give full proofs of the main theorems as they cover basic constructions, Lyapunov exponents and hyperbolicity, dispersing billiards, dynamics of unstable manifolds, ergodic properties, statistical properties, Bunimovich billiards and general focusing chaotic billiards.