By Noether's Theorem we know that any conserved quantity can be associated with a continuous symmetry. I was reading Kepler's Problem and I saw that there can be conserved quantities like Laplace-Runge-Lenz vector which might not be obvious to figure out. So my questions are,
Are there any techniques to find all of the conserved quantities?
How many conserved quantities can a system with $n$ degrees of freedom necessarily have?
Comments on the questions:
Suppose by observations I found some conserved quantities, how can I be sure that I have found all the conserved quantities?
Is there any necessary upper bound?
