By Masayoshi Hata
This exact quantity provides a fruitful and lovely mathematical global hidden in Caianiello's neuronic equations, which describe the instant habit of a version of a mind or considering laptop. The specified research from a standpoint of “dynamical systems”, even in one neuron case, allows us to procure amazingly stable rational approximations to the Hecke–Mahler sequence with variables. a few fascinating numerical functions of our rational approximations also are discussed.
This booklet is essentially self-contained and lots of issues required in it are defined from the start. every one bankruptcy features a variety of instructive and regularly unique routines at a number of levels.
- Basics of Discrete Dynamical Systems
- Caianiello's Equations
- Rotation Numbers
- Classification of B
- Farey Series
- Further research of ƒ ∈ B∞
- Limit units Ωƒ and ωƒ (χ)
- Piecewise Linear Maps
- Orbital and Itinerary Functions
- Farey Structure
- α- and β-Leaves
- Approximations to Hecke–Mahler Series
Readership: Graduates and researchers drawn to dynamical platforms, Farey sequence, Hecke–Mahler sequence, Diophantine approximation (irrationality measures, transcendental numbers).
- A new way to receive “good” rational approximations to features with variables is provided
- A variety of as a rule unique routines is contained in just about all chapters, including their specified recommendations within the “Hints and suggestions” section
- Basic and invaluable mathematical notions in “discrete dynamical systems”, “elementary quantity concept” and in “rational approximation idea” are defined carefully