List of dynamical systems and differential equations topics
# 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
