Return to Answer

Three examples from the theory of dynamical systems (in a broad sense).

• Edward Lorenz' almost accidental discovery of [the first example of a strange attractor] 1 and the butterfly effect.

alt text http://www.levitated.net/daily/laFull1.jpg

• The Fermi-Pasta-Ulam numerical experiments which for the first time exhibited the soliton-like dynamics in a nonlinear system.

• Mitchell Feigenbaum's experiments with iterations of the logistic map which led to the discovery of universality in nonlinear systems.

Three examples from the theory of dynamical systems (in a broad sense).

• Edward Lorenz' almost accidental discovery of [the first example of a strange attractor] 1 and the butterfly effect.

       (source)

• The Fermi-Pasta-Ulam numerical experiments which for the first time exhibited the soliton-like dynamics in a nonlinear system.

• Mitchell Feigenbaum's experiments with iterations of the logistic map which led to the discovery of universality in nonlinear systems.

Three examples from the theory of dynamical systems (in a broad sense).

• Edward Lorenz' almost accidental discovery of [the first example of a strange attractor] 1 and the butterfly effect.

• Fermi, Pasta, Ulam numerical experiments which for the first time exhibited the soliton-like dynamics in a nonlinear system.

• Mitchell Feigenbaum's experiments with iterations of the logistic map which led to the discovery of universality in nonlinear systems.

Three examples from the theory of dynamical systems (in a broad sense).

• Edward Lorenz' almost accidental discovery of [the first example of a strange attractor] 1 and the butterfly effect.

alt text http://www.levitated.net/daily/laFull1.jpg

• The Fermi-Pasta-Ulam numerical experiments which for the first time exhibited the soliton-like dynamics in a nonlinear system.

• Mitchell Feigenbaum's experiments with iterations of the logistic map which led to the discovery of universality in nonlinear systems.

• Edward Lorenz' almost accidental discovery of [the first example of a strange attractor] 1 and the butterfly effect.

• Fermi, Pasta, Ulam numerical experiments for a discretized version of the Korteweg–de Vries equation.

In the Summer of 1953 Fermi, Pasta, Ulam and Mary Tsingou conducted numerical experiments (i.e. computer simulations) of a vibrating string that included a non-linear term (quadratic in one test, cubic in another, and a piecewise linear approximation to a cubic in a third). They found that the behavior of the system was quite different from what intuition would have led them to expect. Fermi thought that after many iterations, the system would exhibit thermalization, an ergodic behavior in which the influence of the initial modes of vibration fade and the system becomes more or less random with all modes excited more or less equally. Instead, the system exhibited a very complicated quasi-periodic behavior.

Three examples from the theory of dynamical systems (in a broad sense).

• Edward Lorenz' almost accidental discovery of [the first example of a strange attractor] 1 and the butterfly effect.

• Fermi, Pasta, Ulam numerical experiments which for the first time exhibited the soliton-like dynamics in a nonlinear system.

• Mitchell Feigenbaum's experiments with iterations of the logistic map which led to the discovery of universality in nonlinear systems.