G. A. Edgar
Fractional Iteration of Series and Transseries.
Fri, 02/12/2010 - 16:01 — SomNambulAuthors: G. A. Edgar
Subjects: Rings and Algebras
AbstractWe investigate compositional iteration of fractional order for transseries.
For any large positive transseries $T$ of exponentiality 0, there is a family
$T^{[s]}$ indexed by real numbers $s$ corresponding to teration of order $s$.
It is based on Abel's Equation. We also investigate the question of whether
there is a family $T^{[s]}$ all sharing a single support set. A subset of the
transseries of exponentiality 0 is divided into three classes ("shallow",
"moderate" and "deep") with different properties related to fractional
iteration.Transseries: Ratios, Grids, and Witnesses.
Tue, 09/15/2009 - 11:27 — SomNambulAuthors: G. A. Edgar
Subjects: Rings and Algebras
AbstractMore remarks and questions on transseries. In particular we deal with the
system of ratio sets and grids used in the grid-based formulation of
transseries. This involves a "witness" concept that keeps track of the ratios
required for each computation. There are, at this stage, questions and missing
proofs in the development.Transseries: Ratios, Grids, and Witnesses.
Tue, 09/15/2009 - 11:27 — SomNambulAuthors: G. A. Edgar
Subjects: Rings and Algebras
AbstractMore remarks and questions on transseries. In particular we deal with the
system of ratio sets and grids used in the grid-based formulation of
transseries. This involves a "witness" concept that keeps track of the ratios
required for each computation. There are, at this stage, questions and missing
proofs in the development.Transseries: Composition, Recursion, and Convergence.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: G. A. Edgar
Subjects: Rings and Algebras
AbstractAdditional remarks and questions for transseries. In particular: properties
of composition for transseries; the recursive nature of the construction of
R[[[ x ]]]; modes of convergence for transseries. There are, at this stage,
questions and missing proofs in the development.Transseries: Composition, Recursion, and Convergence.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: G. A. Edgar
Subjects: Rings and Algebras
AbstractAdditional remarks and questions for transseries. In particular: properties
of composition for transseries; the recursive nature of the construction of
R[[[ x ]]]; modes of convergence for transseries. There are, at this stage,
questions and missing proofs in the development.
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