  Numerical integrations of the Solar System reveal a remarkable stability of
the orbits of the inner planets over billions of years, in spite of their
chaotic variations characterized by a Lyapunov time of only 5 million years and
the lack of integrals of motion able to constrain their dynamics. To open a
window on such long-term behavior, we compute the entire Lyapunov spectrum of a
forced secular model of the inner planets. We uncover a hierarchy of
characteristic exponents that spans two orders of magnitude, manifesting a
slow-fast dynamics with a broad separation of timescales. A systematic analysis
of the Fourier harmonics of the Hamiltonian, based on computer algebra, reveals
three symmetries that characterize the strongest resonances responsible for the
orbital chaos. These symmetries are broken only by weak resonances, leading to
the existence of quasi-integrals of motion that are shown to relate to the
smallest Lyapunov exponents. A principal component analysis of the orbital
solutions independently confirms that the quasi-integrals are among the slowest
degrees of freedom of the dynamics. Strong evidence emerges that they
effectively constrain the chaotic diffusion of the orbits, playing a crucial
role in the statistical stability over the Solar System lifetime.
