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A dynamical system whose evolution is indexed by integer time steps. A single self-map generates forward evolution by iteration; a two-sided integer action requires invertibility.
wp-math-dynamical-systemmit-ocw-nonlinear-dynamicsEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Discrete-time systems specialize the general evolution law to time indexed by or, for reversible dynamics, .
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
wp-math-dynamical-systemmit-ocw-nonlinear-dynamicsThis is an authored directed relation from the source endpoint to the target endpoint.
A self-map generates an -action by iteration, and specifying such a forward discrete action is equivalent to specifying its one-step map. A -action additionally requires an invertible map.
Reinterpret an object, pass to an equivalent presentation, or relate canonically corresponding structures; the carrier may change.
wp-math-dynamical-systemmit-ocw-nonlinear-dynamicsEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
A Poincaré map is a discrete-time dynamical system on a chosen section, but it is defined only on points whose relevant trajectories return and may have a restricted domain.
The target is a member or subtype of the broader source class.
mit-ocw-nonlinear-dynamics