On a Gauss-kuzmin Type Problem for Piecewise Fractional Linear Maps with Explicit Invariant Measure

نویسنده

  • C. GANATSIOU
چکیده

A random system with complete connections associated with a piecewise fractional linear map with explicit invariant measure is defined and its ergodic behaviour is investigated. This allows us to obtain a variant of Gauss-Kuzmin type problem for the above linear map.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Close interval approximation of piecewise quadratic fuzzy numbers for fuzzy fractional program

  The fuzzy approach has undergone a profound structural transformation in the past few decades. Numerous studies have been undertaken to explain fuzzy approach for linear and nonlinear programs. While, the findings in earlier studies have been conflicting, recent studies of competitive situations indicate that fractional programming problem has a positive impact on comparative scenario. We pro...

متن کامل

On Invariant Möbius Measure and Gauss - Kuzmin Face Distribution

Consider an n-dimensional real vector space with lattice of integer points in it. The boundary of the convex hull of all integer points contained inside one of the n-dimensional invariant cones for a hyperbolic n-dimensional linear operator without multiple eigenvalues is called a sail in the sense of Klein. The set of all sails of such n-dimensional operator is called (n−1)-dimensional continu...

متن کامل

A Gauss-Kuzmin Theorem for Continued Fractions Associated with Nonpositive Integer Powers of an Integer m ≥ 2

We consider a family {τ m : m ≥ 2} of interval maps which are generalizations of the Gauss transformation. For the continued fraction expansion arising from τ m , we solve a Gauss-Kuzmin-type problem.

متن کامل

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...

متن کامل

Singular Limits of Absolutely Continuous Invariant Measures for Families of Transitive Maps

We investigate the dependence on the parameters of absolutely continuous invariant measures for a family of piecewise linear piecewise expanding maps. We construct an example to show that the transitivity of the maps does not imply the convergence of those measures to the absolutely continuous invariant measure for the limit map.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2000