I am trying to understand the Arnold conjecture in Symplectic Geometry, which basically tells us the following: If $M$ is a compact symplectic manifold and $H\_t$ be a 1-periodic Hamiltonian function, then we can consider the Hamiltonian equation of motion which defines us a family $\psi\_t$ of symplectomorphisms of $M$. We then consider the fixed points of $\psi\_1$ and call a fixed point $x$ non-degenerate, if $\det(1- d\psi\_1(x)) \neq 0$. In the case that all the fied points are non-degenerate the Arnold conjecture then is: If every fixed point of $\psi\_1$ is non-degenerate, then the number of fixed points is at least the sum off all Betti numbers of $M$. \
I would now like to know the answer to the following questions: \
1. Why is such a result helpful for our understanding of Symplectic Geometry? Why would somebody like to know whether such a conjecture is true or not? \ß
2. Why could this result be true? Can you maybe give me an explanation or reference, why Vladimir Arnold conjectured this result?
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Every answer to the above questions would be appreciated.