  We consider a mechanism for area preserving Hamiltonian systems which leads
to the enhanced probability, $P(\lambda, t)$, to find small values of the
finite time Lyapunov exponent, $\lambda$. In our investigation of chaotic
dynamical systems we go beyond the linearized stability analysis of nearby
divergent trajectories and consider folding of the phase space in the course of
chaotic evolution. We show that the spectrum of the Lyapunov exponents
$F(\lambda)= \lim_{t\to\infty} t^{-1}\ln P(\lambda, t)$ at the origin has a
finite value $F(0)=-\tilde{\lambda}$ and a slope $F'(0)\le 1$. This means that
all negative moments of the distribution $<e^{-m\lambda t}>$ are saturated by
rare events with $\lambda\to 0$. Extensive numerical simulations confirm our
findings.
