Dynamical systems

set of canonical coordinates

bimodal function

scientific theory

system with kinematic constraints that cannot be integrated in position-level constraints

named after Michael Artin and Barry Mazur, a tool for studying the iterated functions that occur in dynamical systems and fractals

type of differential equation in mathematics

a swinging pendulum that is also elastic

parameter in the Mandelbrot set

method for approximating eigenvalues

collection of gravitationally determined pathways through the Solar System that require very little energy for an object to follow

function of seven variables which gives the number of particles per unit volume in single-particle phase space

Micromagnetics is a field of physics dealing with the prediction of magnetic behaviors at sub-micrometer length scales. The length scales considered are large enough for the atomic structure of the material to be ignored (the continuum approximation), yet small enough to resolve magnetic structures such as domain walls or vortices.

under the action of dynamical system

type of system in classical mechanics

phase curve that separates different modes of a dynamical system

visual representation of an iterated function

closed loop through a phase space

concept in theory of differential equations, with applications in control theory

subject of study in ergodic theory

system with no friction or other mechanism to dissipate the dynamics, such that the phase space does not shrink over time

relation in algebra

cellular automaton

diffeomorphism that has a hyperbolic structure on the tangent bundle

in symplectic topology, the theorem that every area-preserving, orientation-preserving homeomorphism of an annulus that rotates the two boundaries in opposite directions has at least two fixed points

thumb|Intermittency in logistic map with r = 3.8282. The trajectory alternates between almost period-3 trajectories and chaotic trajectories. At r = 1 + \sqrt 8 \approx 3.8284 a stable period-3 trajectory emerges. thumb|The intermittency in logistic map can be understood by looking at the cobweb diagram for logistic map (iterated three times). In the cobweb diagram, there are almost-tangencies where the trajectory can be trapped for a long time. thumb|Intermittent jumping between two potential wells in the driven Duffing equation|Duffing oscillator. This is an example of crisis-induced intermi

measure of loss-rate of energy of a mode of oscillation in a dissipative system

sequence satisfying a homogeneous linear recurrence with constant coefficients

type of number sequence

the unification of the theory of difference equations with differential equations

subfield in mathematics

in a dynamical system, a manifold consisting of orbits that do not decay or grow exponentially

continuous-time linear system with only negative real parts

concept in mathematics

set of points linked through the evolution function of a dynamical system

mathematical concept

mathematical concept

Tool in control theory

path between equilibrium points in a phase space

Physical theorem

concept in stability theory

pushforward on the space of measurable functions

mathematical award

Quasiperiodicity is the property of a system that displays irregular periodicity. Periodic behavior is defined as recurring at regular intervals, such as "every 24 hours". Quasiperiodic behavior is almost but not quite periodic. The term used to denote oscillations that appear to follow a regular pattern but which do not have a fixed period. The term thus used does not have a precise definition and should not be confused with more strictly defined mathematical concepts such as an almost periodic function or a quasiperiodic function.

simulation of a dynamical system of bodies, usually under the influence of physical forces and kinematic constraints

portion of phase space of a dynamical system that exhibits stable motion