Dynamical systems

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Dynamical systems
Concepts Core Attractor • Bifurcation • Fractal • Limit set • Lyapunov exponent • orbit • Periodic point • Phase space
Anosov diffeomorphism • Arnold tongue • axiom A dynamical system • Bifurcation diagram • Box-counting dimension • Correlation dimension • Conservative system • Ergodicity • False nearest neighbors • Hausdorff dimension • Invariant measure • Lyapunov stability • Measure-preserving dynamical system • Mixing • Poincaré section • Recurrence plot • SRB measure • Stable manifold • Topological conjugacy
Theorems Ergodic theorem • Liouville's theorem • Krylov-Bogolyubov theorem • Poincaré-Bendixson theorem • Poincaré recurrence theorem • Stable manifold theorem • Takens's theorem
Theoretical
branches
Bifurcation theory • Chaos theory • Control of chaos • Dynamical system • Ergodic theory • Quantum chaos • Stability theory • Synchronization of chaos
Chaotic
maps (list)
Discrete Arnold's cat map • Baker's map • Complex quadratic map • Coupled map lattice • Duffing map • Dyadic transformation • Dynamical billiards • outer • Exponential map • Gauss map • Gingerbreadman map • Hénon map • Horseshoe map • Ikeda map • Interval exchange map • Irrational rotation • Kaplan-Yorke map • Langton's ant • Logistic map • Standard map • Tent map • Tinkerbell map • Zaslavskii map
Continuous Double scroll attractor • Duffing equation • Lorenz system • Lotka-Volterra equations • Mackey-Glass equations • Rabinovich-Fabrikant equations • Rössler attractor • Three-body problem • Van der Pol oscillator
Physical
systems
Chua's circuit • Convection • Double pendulum • Elastic pendulum • FPUT problem • Kicked rotator • Multiscroll attractor • Population dynamics • Swinging Atwood's machine • Tilt-A-Whirl • Weather
Chaos
theorists
Michael Berry • Rufus Bowen • Mary Cartwright • Chen Guanrong • Leon O. Chua • Mitchell Feigenbaum • Peter Grassberger • Celso Grebogi • Martin Gutzwiller • Brosl Hasslacher • Michel Hénon • Svetlana Jitomirskaya • Bryna Kra • Edward Norton Lorenz • Aleksandr Lyapunov • Benoît Mandelbrot • Hee Oh • Edward Ott • Henri Poincaré • Mary Rees • Otto Rössler • David Ruelle • Caroline Series • Yakov Sinai • Oleksandr Mykolayovych Sharkovsky • Nina Snaith • Floris Takens • Audrey Terras • Mary Tsingou • Marcelo Viana • Amie Wilkinson • James A. Yorke • Lai-Sang Young
Related
articles
Butterfly effect • Complexity • Edge of chaos • Predictability • Santa Fe Institute
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