Select any concept, construction junction, or annotated relation by pointer, touch, search, or keyboard.

Construction junctions are diamonds. They show where multiple structures must coexist on the same carrier and satisfy compatibility conditions.

Canonical static concept record

Fixed point of a dynamical system

Open this concept in the interactive graph Read the Markdown equivalent

Summary

A state unchanged by every evolution map. For a discrete system generated by $f$ , it is a point $x$ with $f(x)=x$ ; for a flow, it is an equilibrium trajectory.

Record metadata

Canonical name: Fixed point of a dynamical system
Concept ID: fixed_point_dynamics
Content version: 2.3.0
Primary field: Mathematics
Fields: Mathematics
Primary domain: Dynamical systems
Domains: Dynamical systems
Alternate terminology: No alternate terminology is currently authored for this record.
Concept type: Invariant orbit

Concept sources

Wikipedia — Fixed point (mathematics) — Fixed point (mathematics) · encyclopedic reference · source ID wp-math-fixed-point
Wikipedia — Dynamical system — Dynamical system · encyclopedic reference · source ID wp-math-dynamical-system
MIT OpenCourseWare — Nonlinear Dynamics: Chaos lecture notes — Lecture Notes: Nonlinear Dynamics: Chaos · university lecture notes · source ID mit-ocw-nonlinear-dynamics

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Orbit / trajectory Fixed point of a dynamical system

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: dyn_orbit_to_fixed_point
Relation type: Classification classification
Direction: source → target
Endpoint roles: source: Has subtype; target: Classified as
Authored annotation: stationary orbit

Authored explanation

A fixed point is the orbit consisting of a single state unchanged by the evolution.

How to interpret this relation type

The target is a member or subtype of the broader source class.

Relation sources

Wikipedia — Fixed point (mathematics) — Fixed point (mathematics) · encyclopedic reference · source ID wp-math-fixed-point
Wikipedia — Orbit (dynamics) — Orbit (dynamics) · encyclopedic reference · source ID wp-math-orbit-dynamics
MIT OpenCourseWare — Nonlinear Dynamics: Chaos lecture notes — Lecture Notes: Nonlinear Dynamics: Chaos · university lecture notes · source ID mit-ocw-nonlinear-dynamics

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.