Except for Smale, these studies were all directly inspired by physics: the three-body problem in the case of Birkhoff, turbulence and astronomical problems in the case of Kolmogorov, and radio engineering in the case of Cartwright and Littlewood. Later studies, also on the topic of nonlinear differential equations, were carried out by G.D. Much of the early theory was developed almost entirely by mathematicians, under the name of ergodic theory. In the early 1900s Henri Poincaré, while studying the three-body problem, found that there can be orbits which are nonperiodic, and yet not forever increasing nor approaching a fixed point. In the system studied, Hadamard's billiards, Hadamard was able to show that all trajectories are unstable, in that all particle trajectories diverge exponentially from one another, with a positive Lyapunov exponent.
#CHAOS THEORY MOVIE OST FREE#
The first discoverer of chaos can plausibly be argued to be Jacques Hadamard, who in 1898 published an influential study of the chaotic motion of a free particle gliding frictionlessly on a surface of constant negative curvature. Natural forms in nature (ferns, clouds, mountains, etc.) may be recreated through an Iterated function system (IFS). Bounded chaos is a useful term for describing models of disorder.įractal fern created using chaos game. For example, the Lorenz system pictured is chaotic, but has a clearly defined structure. Recently, another field, called relativistic chaos, has emerged to describe systems that follow the laws of general relativity.Īs well as being orderly in the sense of being deterministic, chaotic systems usually have well defined statistics. A related field of physics called quantum chaos theory studies systems that follow the laws of quantum mechanics. Systems that exhibit mathematical chaos are deterministic and thus orderly in some sense this technical use of the word chaos is at odds with common parlance, which suggests complete disorder. There is some controversy over the existence of chaotic dynamics in the plate tectonics and in economics. Everyday examples of chaotic systems include weather and climate. Observations of chaotic behaviour in nature include the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the dynamics of the action potentials in neurons, and molecular vibrations. 4 Distinguishing random from chaotic dataĬhaotic behavior has been observed in the laboratory in a variety of systems including electrical circuits, lasers, oscillating chemical reactions, fluid dynamics, and mechanical and magneto-mechanical devices.3.3 Minimum complexity of a chaotic system.