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We analytically establish the role of a spectrum of Lyapunov exponents in theevolution of phase-space distributions $\rho(p,q)$. Of particular interest is$\lambda_2$, an exponent which quantifies the rate at which chaoticallyevolving distributions acquire structure at increasingly smaller scales andwhich is generally larger than the maximal Lyapunov exponent $\lambda$ fortrajectories. The approach is trajectory-independent and is thereforeapplicable to both classical and quantum mechanics. In the latter case we showthat the $\hbar\to 0$ limit yields the classical, fully chaotic, result for thequantum cat map.Comment: 5 RevTeX pages + 2 ps figs. Phys. Rev. E (to appear,'97

Chaos and Lyapunov exponents in classical and quantal distribution dynamics