ITM Web Conf.
Volume 34, 2020International Conference on Applied Mathematics and Numerical Methods – third edition (ICAMNM 2020)
|Number of page(s)||7|
|Section||Differential Equations, Dynamical Systems, and Geometry|
|Published online||03 December 2020|
The asymptotic behavior of a dynamical process coming from the development in continuous fractions
University of Craiova, Department of Applied Mathematics Al. I. Cuza 13, Craiova 200585, Dolj, Romania
2 University of Medicine and Pharmacy of Craiova, IT Department Petru Rareş 2, Craiova 200349, Dolj, Romania
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The aim of this paper is the study of a dynamical process generated by a sequence of maps:
where is a a sequence of positive numbers.
This process is generated similar to continuous fractions development.
A continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the inverse of another number, then writing this other number as the sum of its integer part and another inverse, and so on. In a ﬁnite continued fraction (or terminated continued fraction), the iteration is terminated after ﬁnitely many steps by using an integer in stead of another continued fraction. In contrast, an inﬁnite continued fraction is an inﬁnite expression. In either case, all integers in the sequence, other than the ﬁrst, must be positive. The integers are called the coeﬃcients or terms of the continued fraction.
We will study the pre-equilibrium points for this process, the attraction basins and the stability.
Key words: Processes / Lyapunov exponent
© The Authors, published by EDP Sciences, 2020
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