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Chaos Theory Highlights
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Poincaré Map
A method used in the study of dynamical systems by taking intersections of an orbit with a certain lower-dimensional subspace which reduces the continuous dynamics to a discrete map.
Strange Attractor
A non-periodic attractor involved in the chaos theory, which has a fractal structure and is associated with chaotic motion within a dynamical system.
Cantor Set
An example of a fractal, self-similar set that exhibits perfect disorder and zero probability within its structure, often used to teach about chaos in dynamical systems.
Fractal Dimension
A ratio providing a statistical index of complexity comparing how detail in a pattern changes with the scale at which it is measured. It does not have to be an integer.
Lyapunov Exponent
A quantity that characterizes the rate of separation of infinitesimally close trajectories. Positive Lyapunov exponents are an indication of chaos.
Lorenz Attractor
A set of chaotic solutions to the Lorenz equations, which, when plotted, resemble a butterfly or figure eight. It is a fundamental example of deterministic chaos.
Bifurcation
Occurs when a small smooth change made to the parameter values of a system causes a sudden 'qualitative' or topological change in its behavior.
Butterfly Effect
The sensitive dependence on initial conditions, where a small change at one place can result in large differences in a later state. The concept is imagined with a butterfly flapping its wings and causing a typhoon.
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