A multidimensional continued fraction and some of its statistical properties

Journal Article · Sun Mar 01 00:00:00 EST 1992 · Journal of Statistical Physics; (United States)

DOI:https://doi.org/10.1007/BF01054430· OSTI ID:7173571

Baldwin, P R ^[1]

---

1. Univ. of Akron, OH (United States)

The problem of simultaneously approximating a vector of irrational numbers with rationals is analyzed in a geometrical setting using notions of dynamical systems theory. The author discusses here a (vectorial) multidimensional continued-fraction algorithm (MCFA) of additive type, the generalized mediant algorithm (GMA), and gives a geometrical interpretation to it. He calculates the invariant measure of the GMA shift as well as its Kolmogorov-Sinai (KS) entropy for arbitrary number of irrationals. The KS entropy is related to the growth rate of denominators of the Euclidean algorithm. This is the first analytical calculation of the growth rate of denominators for any MCFA.

• DOE Contract Number: AC03-84ER40182
• OSTI ID: 7173571
• Journal Information: Journal of Statistical Physics; (United States), Vol. 66:5-6; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONTINUED FRACTIONS
ALGORITHMS
DYNAMICAL GROUPS
ENTROPY
JACOBIAN FUNCTION
MATHEMATICS
VECTORS
FUNCTIONS
MATHEMATICAL LOGIC
PHYSICAL PROPERTIES
SYMMETRY GROUPS
TENSORS
THERMODYNAMIC PROPERTIES
990200* - Mathematics & Computers
661300 - Other Aspects of Physical Science- (1992-)