Dynamical systems and ergodic theory Basic notions Concept
Iterated function
Summary
An iterated function is a map of a set to itself composed with itself a given number of times. The -th iterate applies exactly times. Iterates are the basic objects of discrete-time dynamics: the state after steps is of the initial state. They also appear in fixed-point iteration, fractals and the study of functional equations.
Where this leads
23 pages build on this one.
- Quadratic polynomial dynamics
- Dynamical Mordell–Lang conjecture
- Cobweb plot
- Discrete-time dynamical system
- Kneser's construction of real analytic tetration
- Attractor
- Iterative root
- Minimal period
- Complex dynamics
- Iterative functional equation
- P-adic dynamics
- Berkovich space dynamics
- Holomorphic dynamics in several variables
- Tetration
- Butterfly effect
- Conservative system
- Fatou set
- Coupled map lattice
- Suspension flow
- Birkhoff sum and average
- Koenigs function
- Periodic point
- Fractional iteration
Further reading
About this page
| Tag | AYVTR2ES5B |
|---|---|
| URI | m2://AYVTR2ES5B |
| Kind | concept |
| Writing | W0 stub |
| MSC | 37B02, 26A18, 37-01 |
| Same as |
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Used by
- Quadratic polynomial dynamics
- Dynamical Mordell–Lang conjecture
- Cobweb plot
- Discrete-time dynamical system
- Attractor
- Iterative root
- Minimal period
- Complex dynamics
- Iterative functional equation
- P-adic dynamics
- Berkovich space dynamics
- Holomorphic dynamics in several variables
- Tetration
- Butterfly effect
- Conservative system
- Fatou set
- Coupled map lattice
- Suspension flow
- Birkhoff sum and average
- Koenigs function
- Periodic point
- Fractional iteration