The Italian physicist Giorgio Parisi (INFN, La Sapienza University of Rome, vice president of the Accademia dei Lincei) takes the Nobel Prize in Physics for his studies on Complex Systems. He shares the Nobel Prize in Physics in half with Syukuro Manabe and Klaus Hasselmann. The two
American ecologist James Cushing discovers chaotic dynamics in tribolium castaneum populations. In the following years these chaotic dynamics will be revealed in many cases of populations of animals, plants, bacteria.
The Chinese mathematician Quidong Wang, who teaches at the Department of Mathematics of the University of Arizona, extends the partial solution to the Three Bodies Problem found in 1912 by the Finnish mathematician Karl Frithiof Sundman to any number of bodies. Sundman had found that the
The key to Chaos is the resonances that amplify small differences
Jacques Laskar of the Bureau des Longitude in Paris shows that the Earth’s orbit is chaotic over a period of 200 million years, that is, it is impossible to calculate where it will be in 200 million years.
Sussman and Wisdom with the Digital Orrery demonstrate the chaos of the Solar System, starting from the simulated orbit of Pluto over 845 million years. Stable deterministic chaos or: non predictability of position and speed but probable (not certain) stability.
With the Digital Orrery the substantial (ie probable) stability of the solar system is demonstrated: deterministic stable chaos or: non predictability of position and speed but probable (not certain) stability.
Edward Belbruno, born in Heidelberg, and who works in Pasadena at JPL, understands that the chaotic dynamics of multi-body problems can be an opportunity for interplanetary travel. He calls the technique Fuzzy Boundary Theory, and in 1990 he will test his theory on the trajectories of
Benoit Mandelbrot creates the famous Mandelbrot Set: practically a catalog of Julia Sets: the black points of the Mandelbrot Sets give rise to unconnected Julia Sets (sse series 0, c, c2 + c, (c2 + c) 2 + c,. .. diverges)
Michel Henon discovers Henon’s strange attractor: x = y + 1-1.4 * x ^ 2; y = 0.3 * x
Werner Karl Heisenberg dies in Munich; on his deathbed he declared: “When I am before God I will ask him two things: why Relativity and why Turbulence; I think He has an answer to the first question …”
Australian ecologist Robert May writes a short article for Nature highlighting and demonstrating that equations commonly used to (correctly) model changes in animal and plant populations in nature can, and quite often, have chaotic behaviors. May’s main tool is the logistic equation. This is a remarkable discovery:
Benoit Mandelbrot: geometric theory of fractals
Martin Gardner explains in a famous article in Scientific American, John Conway’s LIFE game, or the most famous example of Cellular Automata; the rules are only 2: if a cell is alive and has 2 or 3 living cells nearby, then it survives (otherwise it dies); 3
Edward Lorenz demonstrates that the dynamics of chaos are extremely sensitive to initial conditions.
Edward Lorenz demonstrates the limits of the predictability of meteorology (part of the Chaos theory)
Edward Lorenz discovers strange attractors
The problem of the 3 bodies, Vladimir Arnol’d and Jurgen Moser are attacked, with the so-called KAM theorem, from their initials and that of Andrei Kolmogorov who in 1954 had indicated the guidelines for dealing with it. Henri Poincare ‘had already faced the problem at the
The problem of the 3 bodies, is attacked from the chest by Andrei Kolmogorov who indicates the guidelines for dealing with it. His program will be carried out by Vladimir Arnol’d and Jurgen Moser in 1962 in the so-called KAM theorem. Henri Poincare had already tackled the
The Englishman B. Thomas discovers that the friction of water in pipes can be greatly reduced by using small (1%) quantities of polymers dissolved in the water; the long chains of polymers, in fact, disfavour the formation of vortices and turbulences that would slow down the
Birkhoff develops the Chaos Theory
The French Gaston Julia and Pierre Fatou discover the fractal figures then called Julia Sets: the colored points (inside the prisoner set) if subjected to the z2 + c transformation remain confined to the prisoner set, the points external to it diverge indefinitely
Finnish mathematician Karl Frithiof Sundman discovers that the presence of chaos does not rule out series-based solutions, but these are almost always valid, rather than valid. Apply the concept to the Three Bodies Problem. Its series converge unless the moment of the momentum is zero in the
Fractals: Georg Cantor creates Cantor’s Dust (a line is divided into three parts, two black and one transparent, ad infinitum); Sierpinsky carpet (a square is divided into 9 squares and the central one removed, ad infinitum); Sponge by Menger (it is the Sierpinsky carpet applied in 3D
The Swedish Helge Van Koch creates the Koch Ribbon: a triangle on whose sides another triangle ad infinitum is obtained, a fractal figure with dimension 1.2618
Henri Poincare ‘publishes the trilogy “The new methods of Celestial Mechanics” which deal in particular with the topological study of nonlinear differential equations and the apparent chaotic behavior of their solutions depending on small changes in the initial conditions.
Henri Poincare ‘revises his thesis on Acta Mathematica: the solar system is stable and inaugurates the notion of Dynamic Chaos