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We discuss classical magnetotransport in a two-dimensional system with strongscatterers. Even in the limit of very low field, when $\omega_c \tau \ll 1$($\omega_c$ is the cyclotron frequency, $\tau$ is the scattering time) such asystem demonstrates strong negative magnetoresistance caused by non-Markovianmemory effects. A regular method for the calculation of non-Markoviancorrections to the Drude conductivity is presented. A quantitative theory ofthe recently discovered anomalous low-field magnetoresistance is developed forthe system of two-dimensional electrons scattered by hard disks of radius $a,$randomly distributed with concentration $n.$ For small magnetic fields themagentoresistance is found to be parabolic and inversely proportional to thegas parameter, $ \delta \rho_{xx}/\rho \sim - (\omega_c \tau)^2 / n a^2.$ Insome interval of magnetic fields the magnetoresistance is shown to be linear$\delta \rho_{xx}/\rho \sim - \omega_c \tau $ in a good agreement with theexperiment and numerical simulations. Magnetoresistance saturates for $\omega_c\tau \gg na^2$, when the anomalous memory effects are totally destroyed by themagnetic field. We also discuss magnetotransport at very low fields and showthat at such fields magnetoresistance is determined by the trajectories havinga long Lyapunov region.Comment: 22 pages, 16 figure

Non-Markovian effects on the two-dimensional magnetotransport: Low-field anomaly in magnetoresistance