Transseries and Real Differential Algebra
Hoeven, Joris van der.
Transseries and Real Differential Algebra [electronic resource] / by Joris van der Hoeven. - XII, 260 p. 8 illus. online resource. - Lecture Notes in Mathematics, 1888 0075-8434 ; . - Lecture Notes in Mathematics, 1888 .
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.
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 in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in Écalle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists.
9783540355915
10.1007/3-540-35590-1 doi
Geometry, algebraic.
Functional equations.
Differentiable dynamical systems.
Algebraic Geometry.
Difference and Functional Equations.
Dynamical Systems and Ergodic Theory.
QA564-609
516.35
Transseries and Real Differential Algebra [electronic resource] / by Joris van der Hoeven. - XII, 260 p. 8 illus. online resource. - Lecture Notes in Mathematics, 1888 0075-8434 ; . - Lecture Notes in Mathematics, 1888 .
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.
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 in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in Écalle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists.
9783540355915
10.1007/3-540-35590-1 doi
Geometry, algebraic.
Functional equations.
Differentiable dynamical systems.
Algebraic Geometry.
Difference and Functional Equations.
Dynamical Systems and Ergodic Theory.
QA564-609
516.35