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 Quadratic rational rotations of the torus and dual lattice maps
 摘  要: We develop a general formalism for computed-assisted proofs concerning the orbit structure of certain non ergodic piecewise ane 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 8 maps), then the periodic orbits are organized into nitely 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.
 发  表: Nonlinearity  2002

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 共享有3个版本 http://dx.doi.org/10.1088/0951-7715/15/6/306 http://stacks.iop.org/0951-7715/15/i=6/a=306?key=crossref.47bec31dbbe07b69550799d1f4c42a71 http://www.ma.utexas.edu/mp_arc/c/02/02-148.ps.gz
 Bibtex @article{50654, author = {K. L. Kouptsov and J. H. Lowenstein and F. Vivaldiy}, title = {{Quadratic rational rotations of the torus and dual lattice maps}}, journal = {Nonlinearity}, volume = {15}, year = {2002}, pages = {1795--1842}, issue = {6}, doi = {10.1088/0951-7715/15/6/306} }

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