# List of dynamical systems and differential equations topics

This is a list of dynamical system and differential equation topics, by Wikipedia page. See also list of partial differential equation topics, list of equations.

## Dynamical systems, in general

* Deterministic system (mathematics)
* Linear system
* Partial differential equation
* Dynamical systems and chaos theory
* Chaos theory
** Chaos argument
** Butterfly effect
** 0-1 test for chaos
* Bifurcation diagram
* Feigenbaum constant
* Sharkovskii's theorem
* Attractor
** Strange nonchaotic attractor
* Stability theory
** Mechanical equilibrium
** Astable
** Monostable
** Bistability
** Metastability
* Feedback
** Negative feedback
** Positive feedback
** Homeostasis
* Damping ratio
* Dissipative system
* Spontaneous symmetry breaking
* Turbulence
* Perturbation theory
* Control theory
** Non-linear control
** Adaptive control
** Hierarchical control
** Intelligent control
** Optimal control
** Dynamic programming
** Robust control
** Stochastic control
* System dynamics, system analysis
* Takens' theorem
* Exponential dichotomy
* Liénard's theorem
* Krylov–Bogolyubov theorem
* Krylov-Bogoliubov averaging method

## Abstract dynamical systems

* Measure-preserving dynamical system
* Ergodic theory
* Mixing (mathematics)
* Almost periodic function
* Symbolic dynamics
* Time scale calculus
* Arithmetic dynamics
* Sequential dynamical system
* Graph dynamical system
* Topological dynamical system

## Dynamical systems, examples

* List of chaotic maps
* Logistic map
* Lorenz attractor
* Lorenz-96
* Iterated function system
* Tetration
* Ackermann function
* Horseshoe map
* Hénon map
* Arnold's cat map
* Population dynamics

## Complex dynamics

* Fatou set
* Julia set
* Mandelbrot set

## Difference equations

* Recurrence relation
* Matrix difference equation
* Rational difference equation

## Ordinary differential equations: general

* Examples of differential equations
* Autonomous system (mathematics)
* Picard–Lindelöf theorem
* Peano existence theorem
* Carathéodory existence theorem
* Numerical ordinary differential equations
* Bendixson–Dulac theorem
* Gradient conjecture
* Recurrence plot
* Limit cycle
* Initial value problem
* Clairaut's equation
* Singular solution
* Poincaré–Bendixson theorem
* Riccati equations
* Functional differential equation

## Linear differential equations

* Exponential growth
** Malthusian catastrophe
* Exponential response formula
* Simple harmonic motion
** Phasor (physics)
** RLC circuit
** Resonance
*** Impedance
*** Reactance
*** Musical tuning
*** Orbital resonance
*** Tidal resonance
* Oscillator
** Harmonic oscillator
** Electronic oscillator
** Floquet theory
** Fundamental frequency
** Oscillation (Vibration)
* Fundamental matrix (linear differential equation)
* Laplace transform applied to differential equations
* Sturm–Liouville theory
* Wronskian
* Loewy decomposition

## Mechanics

* Pendulum
** Inverted pendulum
** Double pendulum
** Foucault pendulum
** Spherical pendulum
* Kinematics
* Equation of motion
* Dynamics (mechanics)
* Classical mechanics
* Isolated physical system
** Lagrangian mechanics
** Hamiltonian mechanics
** Routhian mechanics
** Hamilton-Jacobi theory
** Appell's equation of motion
** Udwadia–Kalaba equation
** Celestial mechanics
** Orbit
* Lagrange point
** Kolmogorov-Arnold-Moser theorem
** N-body problem, many-body problem
* Ballistics

## Functions defined via an ODE

* Airy function
* Bessel function
* Legendre polynomials
* Hypergeometric function

## Rotating systems

* Angular velocity
* Angular momentum
* Angular acceleration
* Angular displacement
* Rotational invariance
* Rotational inertia
* Torque
* Rotational energy
* Centripetal force
* Centrifugal force
** Centrifugal governor
* Coriolis force
* Axis of rotation
* Flywheel
** Flywheel energy storage
** Momentum wheel
* Spinning top
* Gyroscope
* Gyrocompass
* Precession
* Nutation

## Swarms

* Particle swarm optimization
* Self-propelled particles
* Swarm intelligence

## Stochastic dynamic equations

* Random walk
* Autoregressive process
* Unit root
* Moving average process
* Autoregressive–moving-average model
* Autoregressive integrated moving average
* Vector autoregressive model
* Stochastic differential equation
* Stochastic partial differential equation