Rational approximations, multidimensional continued fractions and lattice reduction

We first survey the current state of the art concerning the dynamical properties of multidimensional continued fraction algorithms defined dynamically as piecewise fractional maps and compare them with algorithms based on lattice reduction. We discuss their convergence properties and the quality of the rational approximation, and stress the interest for these algorithms to be obtained by iterating dynamical systems. We then focus on an algorithm based on the classical Jacobi--Perron algorithm involving the nearest integer part. We describe its Markov properties and we suggest a possible procedure for proving the existence of a finite ergodic invariant measure absolutely continuous with respect to Lebesgue measure.Comment: 30 pages, 4 figure

CIMODE 2016: 3º Congresso Internacional de Moda e Design: proceedings

O CIMODE 2016 é o terceiro Congresso Internacional de Moda e Design, a decorrer de 9 a 12 de maio de 2016 na cidade de Buenos Aires, subordinado ao tema : EM--‐TRAMAS. A presente edição é organizada pela Faculdade de Arquitetura, Desenho e Urbanismo da Universidade de Buenos Aires, em conjunto com o Departamento de Engenharia Têxtil da Universidade do Minho e com a ABEPEM – Associação Brasileira de Estudos e Pesquisa em Moda.info:eu-repo/semantics/publishedVersio