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- W1991201650 abstract "We develop a general formalism for computer-assisted proofs concerning the orbit structure of certain nonergodic piecewise affine maps of the torus, whose eigenvalues are roots of unity. For a specific class of maps, we prove that if the trace is a quadratic irrational (the simplest nontrivial case, comprising eight maps), then the periodic orbits are organized into finitely many renormalizable families, with exponentially increasing period, plus a finite number of exceptional families. The proof is based on exact computations with algebraic numbers, where units play the role of scaling parameters. Exploiting a duality existing between these maps and lattice maps representing rounded-off planar rotations, we establish the global periodicity of the latter systems, for a set of orbits of full density." @default.
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- W1991201650 date "2002-09-16" @default.
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- W1991201650 title "Quadratic rational rotations of the torus and dual lattice maps" @default.
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