about the logo
by Dr. M. A. Trump of the Ilya Prigogine Center
The Center's website logo is a stylized rendering of one of the most popular and well-studied systems of modern dynamics, namely the Standard Map. The Standard Map represents the motion in time of a simple rotating system disturbed by an outside kicking force from a fixed direction in space at exactly regular intervals in time. In each of the three panels, the angular position of the rotor is plotted along the horizontal axis, while the angular speed is plotted along the vertical axis. Each panel depicts the motion in time of the rotor for ten different starting conditions of position and speed. The position and speed of the rotor are measured at later times as if seen in a strobe light that goes off at regular intervals, a common plotting device in nonlinear dynamics. From left to right, the three panels depict the time behavior of the rotating object for three cases of increasing strength of the kicking force. For weak kicking strength, the strobe-sampled measurements of the rotating object trace out an ordered structure as they unfold in time, as in the green panel at left. If the kicking strength is increased, the strobe-sampled measurements begin to trace out a less-ordered structure, as in the blue panel in the center. If the kicking strength is increased above a certain critical threshold, the pattern traced out by the strobe-sampled measurements loses all its structure over a region covering most of the graph, resulting in chaotic motion, as seen in the red panel at right.

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For more information on the Standard Map, see
L. E. Reichl, The Transition to Chaos in Conservative Classical Systems: Quantum Manifestations
(Springer-Verlag, N.Y.,1992)