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We consider the ground state configurations of the Josephson vortex lattice in layered superconductors. Due to commensurability effects with the layered structure, the lattice has multiple configurations, both aligned with layers and rotated at finite angle. At low fields the lattice switches between these configurations via first-order phase transitions. These transitions become more frequent at smaller fields. With increasing magnetic field a dilute lattice transforms first into a sheared dense lattice. With further increase of field, the shear deformation smoothly vanishes at a second-order phase transition.

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