Exercise #2

a) Ergodic flow map: Consider the exercise 6.4 of the Reichl’s book:

Reichl6.4.png

  • Find a conserved quantity.

  • Find the stationary distribution function.

  • Are volumes of phase pace conserved?

  • Choose an observable f(p,q)

  • Is the system ergodic w.r.t. that observable?

  • By choosing an ensemble of initial states is the system mixing?

b) Consider the Arnold’s cat map.

  • Find the stationary distribution function.

  • Are volumes of phase pace conserved?

  • Choose an observable f(p,q)

  • Is the system ergodic w.r.t. that observable?

  • By choosing an ensemble of initial states is the system mixing?

  • Could you find a recurrence time for this map?