Dynamics of a quasi-quadratic map

• Tipo: Artigo em Revista Científica Internacional
• Data: 2014

Autores

Assis Azevedo (Autor) Outra; Maria Carvalho (Autor) FCUP; Antonio Machiavelo (Autor) FCUP

Revista

Título: Journal of Difference Equations and Applications

Vol. 20 Nº 1

Páginas: 36-48

ISSN: 1023-6198

Editora: Taylor & Francis

Indexação

ISI Web of Knowledge - 1 Citação

Scopus - 0 Citações

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

CORDIS: Ciências Físicas > Matemática > Teoria dos números

Outras Informações

ID Authenticus: P-008-FKS

DOI: 10.1080/10236198.2013.805754

Abstract (EN): We consider the map X : Q --> Q given by X(x) = inverted right perpendicularxinverted left perpendicular, where inverted right perpendicular x inverted left perpendicular denotes the smallest integer greater than or equal to x, and study the problem of finding, for each rational, the smallest number of iterations by x that sends it into an integer. Given two natural numbers M and n, we prove that the set of numerators of the irreducible fractions that have denominator M and whose orbits by x reach an integer in exactly n iterations is a disjoint union of congruence classes modulo Mn+1. Moreover, we establish a finite procedure to determine them. We also describe an efficient algorithm to decide whether an orbit of a rational number bigger than one fails to hit an integer until a prescribed number of iterations have elapsed, and deduce that the probability that such an orbit enters Z is equal to 1.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 13