Transseries and Real Differential Algebra

• Main Author: Hoeven, Joris van der (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Series: Lecture Notes in Mathematics, 1888
• Subjects: Mathematics.; Algebraic geometry.; Difference equations.; Functional equations.; Dynamics.; Ergodic theory.; Algebraic Geometry.; Difference and Functional Equations.; Dynamical Systems and Ergodic Theory.

Transseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm. They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equations and find their origin...

Table of Contents:

• Orderings
• Grid-based series
• The Newton polygon method
• Transseries
• Operations on transseries
• Grid-based operators
• Linear differential equations
• Algebraic differential equations
• The intermediate value theorem.