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.

Contents 1 Dynamical systems, in general 2 Abstract dynamical systems 3 Dynamical systems, examples 4 Complex dynamics 5 Difference equations 6 Ordinary differential equations: general 7 Linear differential equations 8 Mechanics 9 Functions defined via an ODE 10 Rotating systems 11 Swarms 12 See also

Dynamical systems, in general

• Deterministic system (mathematics)
• Linear system
• Dynamical systems and chaos theory
• Chaos theory
  • Chaos argument
  • Butterfly effect
• Bifurcation diagram
• Feigenbaum constant
• Sarkovskii's theorem
• Attractor
• Stability theory
  • Mechanical equilibrium
  • Astable
  • Monostable
  • Bistable
  • 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
  • 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-95
• 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

Linear differential equations

• Exponential growth
  • Malthusian catastrophe
• 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
  • Vibration
• Laplace transform applied to differential equations
• Sturm–Liouville theory
• Wronskian

Mechanics

• Pendulum
  • Inverted pendulum
  • Double pendulum
  • Foucault pendulum
  • Spherical pendulum
• Kinematics
• Equation of motion
• Dynamics (mechanics)
• Classical mechanics
• Isolated physical system
  • Lagrangian mechanics
    • Lagrangian
  • Hamiltonian mechanics
  • 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

See also

• differential equations from outside physics
• differential equations of mathematical physics