Dynamical system

related topics
{math, energy, light}
{math, number, function}
{water, park, boat}
{style, bgcolor, rowspan}

A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each spring in a lake.

At any given time a dynamical system has a state given by a set of real numbers (a vector) which can be represented by a point in an appropriate state space (a geometrical manifold). Small changes in the state of the system correspond to small changes in the numbers. The evolution rule of the dynamical system is a fixed rule that describes what future states follow from the current state. The rule is deterministic; in other words, for a given time interval only one future state follows from the current state.

Contents

Full article ▸

related documents
Dimensional analysis
Lorentz transformation
Noether's theorem
Quantum superposition
Quantum entanglement
Wave equation
Mathematical formulation of quantum mechanics
Statistical mechanics
Symmetry
Platonic solid
Shape of the Universe
Perturbation theory
Kepler's laws of planetary motion
List of relativistic equations
Quantum computer
Phonon
Phase transition
Kinetic energy
Variable star
Wave
Proxima Centauri
Nonlinear optics
Gamma ray burst
Tau Ceti
Electric field
Eclipse
Event horizon
Longitude
Holographic principle
Orbital resonance