In the theory of In engineering and mathematics, a dynamical system is a deterministic process in which a functions value changes over time according to a rule that is defined in terms of the functions current value. ...dynamical systems, a Poincaré map is the intersection of a In ordinary language, a trajectory is the path followed by a body moving through space, for instance, the path taken by a falling body or the orbit of a planet. ...trajectory of something which moves In mathematics, a periodic function is a function that repeats its values, after adding some definite period to the variable. ...periodically (or quasi_periodically, or Chaos theory, in mathematics and physics, deals with the behavior of certain nonlinear dynamical systems that (under certain conditions) exhibit the phenomenon known as chaos, most famously characterised by sensitivity to initial conditions (see butterfly effect). ...chaotically), in a space of at least three dimensions, with a In geometry, a hyperplane is a linear, affine, or projective subspace of codimension 1. ...hyperplane of one fewer dimension. More precisely, one observes the return of the trajectory to the hyperplane which starts at a given point of it. The name is for Henri Poincaré, photograph from the frontispiece of the 1913 edition of Last Thoughts Jules Henri Poincaré ( April 29, 1854 – July 17, 1912) was one of Frances greatest mathematicians, theoretical scientists and a philosopher of science. ...Henri Poincaré.

It differs from a Natural processes can have a distinct recurrent behaviour, e. ...recurrence plot in that space, not time, determines when to plot a point. For instance, the locus of the moon when the earth is at This article is about several astronomical terms (apogee & perigee, aphelion & perihelion, generic equivalents based on apsis, and related but rarer terms. ...perihelion is a recurrence plot; the locus of the moon when it passes through the plane perpendicular to the earth's orbit and passing through the sun and the earth at perihelion is a Poincaré map. It was used by Michel Hénon to study the motion of stars in a This article is about a celestial body. ...galaxy, because the path of a star projected on a plane looks like a tangled mess, while the Poincaré map shows the structure more clearly.

See also

• In engineering and mathematics, a dynamical system is a deterministic process in which a functions value changes over time according to a rule that is defined in terms of the functions current value. ...dynamical systems
• stroboscopic map
• The Hénon map is a discrete_time dynamical system. ...Hénon map

External links

• http://www.drchaos.net/drchaos/Book/node101.html