Linear mod one transformations and the distribution of fractional parts {ξ(p/q)n}

Invariant Measures for Certain Linear Fractional Transformations Mod 1

Explicit invariant measures are derived for a family of finite-toone, ergodic transformations of the unit interval having indifferent periodic orbits. Examples of interesting, non-trivial maps of [0, 1] for which one can readily compute an invariant measure absolutely continuous to Lebesgue measure are not easy to come by. The familiar examples are the Gauss map, the backward continued fraction...

on the effect of linear & non-linear texts on students comprehension and recalling

چکیده ندارد.

On One-Sided Ideals of Rings of Linear Transformations

Orbit Representations from Linear mod 1 Transformations

We show that every point x0 ∈ [0, 1] carries a representation of a C∗-algebra that encodes the orbit structure of the linear mod 1 interval map fβ,α(x) = βx + α. Such C∗-algebra is generated by partial isometries arising from the subintervals of monotonicity of the underlying map fβ,α. Then we prove that such representation is irreducible. Moreover two such of representations are unitarily equi...

Contractivity of linear fractional transformations

One possible approach to exact real arithmetic is to use linear fractional transformations (LFT's) to represent real numbers and computations on real numbers. Recursive expressions built from LFT's are only convergent (i.e., denote a well-deened real number) if the involved LFT's are suuciently contractive. In this paper, we deene a notion of contrac-tivity for LFT's. It is used for convergence...