geodesic flow
1Geodesic — [ great circle arcs.] In mathematics, a geodesic IPA|/ˌdʒiəˈdɛsɪk, ˈdisɪk/ [jee uh des ik, dee sik] is a generalization of the notion of a straight line to curved spaces . In presence of a metric, geodesics are defined to be (locally) the… …
2Flow (mathematics) — In mathematics, a flow formalizes, in mathematical terms, the general idea of a variable that depends on time that occurs very frequently in engineering, physics and the study of ordinary differential equations. Informally, if x(t) is some… …
3Vector flow — In mathematics, the vector flow refers to a set of closely related concepts of the flow determined by a vector field. These appear in a number of different contexts, including differential topology, Riemannian geometry and Lie group theory. These …
4Closed geodesic — In differential geometry and dynamical systems, a closed geodesic on a Riemannian manifold M is the projection of a closed orbit of the geodesic flow on M. Contents 1 Examples 2 Definition 3 See also 4 …
5Prime geodesic — In mathematics, a prime geodesic on a hyperbolic surface is a primitive closed geodesic, i.e. a geodesic which is a closed curve that traces out its image exactly once. Such geodesics are called prime geodesics because, among other things, they… …
6Zonal flow (plasma) — In toroidally confined fusion plasma experiments the term zonal flow means a plasma flow within a magnetic surface primarily in the poloidal direction. This usage is inspired by the analogy between the quasi two dimensional nature of large scale… …
7Anosov diffeomorphism — In mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold M is a certain type of mapping, from M to itself, with rather clearly marked local directions of expansion and contraction .… …
8Geodesics as Hamiltonian flows — In mathematics, the geodesic equations are second order non linear differential equations, and are commonly presented in the form of Euler–Lagrange equations of motion. However, they can also be presented as a set of coupled first order equations …
9Ergodic theory — is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics. A central concern of ergodic theory is the behavior of a dynamical …
10Glossary of Riemannian and metric geometry — This is a glossary of some terms used in Riemannian geometry and metric geometry mdash; it doesn t cover the terminology of differential topology. The following articles may also be useful. These either contain specialised vocabulary or provide… …
