Problem 3. Dynamics in phase space. We consider the following equations of motion (t) ax(t) (p(t) - 1). p(t)p(t) (1x(t)) where a is a positive real number, and x(t), p(t) are real-valued funktions. a) Determine the fixed points of the dynamics, i.e. points (To. Po) where (i(t), p(t)) (()))=(ro.po)=0. b) Show that Iz(t) + a p(t) In(r(t) p(t)) is a constant of motion of the dynamics, i.e. = 0. **c) For small one has 1+- In(1+)1 + 2/2. Use this information to sketch the phase space trajectories of the dynamics. ** d) Provide and argument why the functions (t) and p(t) can not be considered as the position and the momentum of a particle.