Chapter 2 Trajectories Poetry is what is lost in translation

Abstract:  e space or phase space M. As the system changes, so does the representative point in phase space. We refer to the evolution of such points as dynamics, and the function ft which specifies where the representative point is at time t as the evolution rule. If there is a definite rule f that tells us how this representative point moves in A/, the system is said to be deterministic. For a deterministic dynamical system the evolution rule takes one point of the phase space and maps it into another point. Not two or three, but exactly one. This is not always possible. For example, knowing the temperature today is not enough to predict the temperature tommorrow; or knowing the value of a stock market index today will not determine its value tommorrow. The phase space can be enlarged, in the hope that in a sufficently large phase space it is possible to determine an evolution rule, so we imagine that knowing the state of the atmosphere measured over many points over the entire planet should b