Asymptotic Differential Algebra and Model Theory of Transseries : (AMS-195) /

Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logar...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Aschenbrenner, Matthias (Autor), van den Dries, Lou (Autor), van der Hoeven, Joris (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, NJ : Princeton University Press, [2017]
Colección:Annals of Mathematics Studies ; 195
Temas:
Asymptotic expansions.
Differential algebra.
Divergent series.
Series, Arithmetic.
MATHEMATICS / Algebra / Abstract.
Equalizer Theorem.
H-asymptotic couple.
H-asymptotic field.
H-field.
Hahn Embedding Theorem.
Hahn space.
Johnson's Theorem.
Krull's Principal Ideal Theorem.
Kähler differentials.
Liouville closed H-field.
Liouville closure.
Newton degree.
Newton diagram.
Newton multiplicity.
Newton tree.
Newton weight.
Newton-Liouville closure.
Riccati transform.
Scanlon's extension.
Zariski topology.
algebraic differential equation.
algebraic extension.
angular component map.
asymptotic couple.
asymptotic differential algebra.
asymptotic field.
asymptotic relation.
asymptotics.
closed H-asymptotic couple.
closure properties.
coarsening.
commutative algebra.
commutative ring.
compositional conjugation.
constant.
continuity.
d-henselian.
d-henselianity.
decomposition.
derivation.
differential field extension.
differential field.
differential module.
differential polynomial.
differential-hensel.
differential-henselian field.
differential-henselianity.
differential-valued extension.
differentially closed field.
dominant part.
equivalence.
eventual quantities.
exponential integral.
extension.
filtered module.
gaussian extension.
grid-based transseries.
henselian valued field.
homogeneous differential polynomial.
immediate extension.
integral.
integrally closed domain.
linear differential equation.
linear differential operator.
linear differential polynomial.
mathematics.
maximal immediate extension.
model companion.
monotonicity.
noetherian ring.
ordered abelian group.
ordered differential field.
ordered set.
pre-differential-valued field.
pseudocauchy sequence.
pseudoconvergence.
quantifier elimination.
rational asymptotic integration.
regular local ring.
residue field.
simple differential ring.
small derivation.
special cut.
specialization.
substructure.
transseries.
triangular automorphism.
triangular derivation.
valuation topology.
valuation.
value group.
valued abelian group.
valued differential field.
valued field.
valued vector space.
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