List of dynamical systems and differential equations topics

Dynamical systems, in general

• Deterministic system
• 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
• 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
• 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 equation]s: general

• Examples of differential equations
• Autonomous system
• 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 equation]s

• Exponential growth
• *Malthusian catastrophe
• Exponential response formula
• Simple harmonic motion
• *Phasor
• *RLC circuit
• *Resonance
• **Impedance
• **Reactance
• **Musical tuning
• **Orbital resonance
• **Tidal resonance
• Oscillator
• *Harmonic oscillator
• *Electronic oscillator
• *Floquet theory
• *Fundamental frequency
• *Oscillation
• Fundamental matrix
• 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
• 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