By Jean-René Chazottes, Bastien Fernandez
This ebook is ready the dynamics of coupled map lattices (CML) and of similar spatially prolonged platforms. it will likely be valuable to post-graduate scholars and researchers looking an outline of the state of the art and of open difficulties during this zone of nonlinear dynamics. The detailed function of this ebook is that it describes the (mathematical) concept of CML and a few similar platforms and their phenomenology, with a few examples of CML modeling of concrete structures (from physics and biology). extra accurately, the booklet offers with statistical homes of (weakly) coupled chaotic maps, geometric features of (chaotic) CML, monotonic spatially prolonged structures, and dynamical versions of particular organic systems.
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Dr = 0 C for every loop C, or equivalently that rot f = 0. }. This is the case for weight, for electric force but not for friction. A system that undergoes only conservative forces is hamiltonian. The equations that govern its dynamics are the Hamilton equations: where function H(q,p,t) is called hamiltonian of the system.
Typically the state is compound by: photons, atoms, molecules and electrons. The radiative epoch ends by definition when there are no more free electrons. Light and matter are thus decoupled. This is the origin of the cosmic background radiation. Universe becomes "transparent" (to photons). Photons does no more colide with electrons. 51010 years, T = 3K), Universe enters the stellar epoch. This is now the kingdom of the gravitation. Because of (unexplained) fluctuations is the gas density, particles (atoms and molecules) begin to gather under gravitation to for prostars and stars.
A kinetic description of system constituted by an large number of particles consists in representing the state of considered system by a function f(r,p,t) called "repartition" function, that represents the probability density to encounter a particle at position r with momentum p. }. Space geometrization Classical mechanics Classical mechanics is based on two fundamental principles: the {\bf Galileo relativity} principle {Galileo relativity} and the fundamental principle of dynamics. Let us state Galileo relativity principle: Principle: Galileo relativity principle.