By Ovidiu Costin, Frédéric Fauvet, Frédéric Menous, David Sauzin

Those are the court cases of a one-week overseas convention headquartered on asymptotic research and its purposes. They include significant contributions facing - mathematical physics: PT symmetry, perturbative quantum box thought, WKB research, - neighborhood dynamics: parabolic structures, small denominator questions, - new facets in mold calculus, with similar combinatorial Hopf algebras and alertness to multizeta values, - a brand new kin of resurgent features regarding knot conception.

**Read or Download Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation, Vol. I PDF**

**Similar differential geometry books**

**Geometry of Some Special Arithmetic Quotients**

The ebook discusses a chain of higher-dimensional moduli areas, of abelian kinds, cubic and K3 surfaces, that have embeddings in projective areas as very targeted algebraic types. lots of those have been identified classically, yet within the final bankruptcy a brand new such style, a quintic fourfold, is brought and studied.

The contributions making up this quantity are improved models of the classes given on the C. I. M. E. summer season university at the idea of Moduli.

**Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation, Vol. I**

Those are the complaints of a one-week foreign convention situated on asymptotic research and its purposes. They comprise significant contributions facing - mathematical physics: PT symmetry, perturbative quantum box thought, WKB research, - neighborhood dynamics: parabolic platforms, small denominator questions, - new features in mold calculus, with similar combinatorial Hopf algebras and alertness to multizeta values, - a brand new family members of resurgent capabilities relating to knot conception.

**Topology II: Homotopy and Homology. Classical Manifolds**

To Homotopy thought O. Ya. Viro, D. B. Fuchs Translated from the Russian by means of C. J. Shaddock Contents bankruptcy 1. easy suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . four § 1. Terminology and Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- Handbook of Geometric Analysis,
- A Treatise on the Differential Geometry of Curves and Surfaces
- Comprehensive Introduction to Differential Geometry
- Contact Manifolds in Riemannian Geometry
- Quaternionic structures in mathematics and physics: proceedings of the second meeting: Rome, Italy, 6-10 September 1999
- Lectures on Probability Theory and Statistics: Ecole d’Ete de Probabilites de Saint-Flour XXV - 1995

**Extra info for Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation, Vol. I**

**Sample text**

3 The four gates to the inner algebra . . . . 2 Some resurgence background . . . . . . . . 1 Resurgent functions and their three models . . 2 Alien derivations as a tool for Riemann surface description . . . . . . . . . . 3 Retrieving the resurgence of a series from the resurgence of its Taylor coefÀcients . . . . 3 The ingress factor . . . . . . . . . . . 1 Bernoulli numbers and polynomials . . . . 2 Resurgence of the Gamma function . . . . 3 Monomial/binomial/exponential factors .

2) ( ∈ {0, 1}). Summation starts at = 0 unless F(0) ∈ {0, ∞}, in which case it starts at = 1. 1 The two driving functions F 1 This choice is to ensure near-invariance under the change F(x) → 1/F(1 − x). 5. 38 Jean Ecalle and Shweta Sharma and f are connected under F ≡ exp(− f ). e. when f is holomorphic. ). As for the above deÀnition, it is less arbitrary than may seem at Àrst sight. Indeed, none of the following changes: (i) changing the grid {k/n} to {Const k/n} (ii) changing the lower summation bounds from 0 or 1 to 2,3 .

2) ( ∈ {0, 1}). Summation starts at = 0 unless F(0) ∈ {0, ∞}, in which case it starts at = 1. 1 The two driving functions F 1 This choice is to ensure near-invariance under the change F(x) → 1/F(1 − x). 5. 38 Jean Ecalle and Shweta Sharma and f are connected under F ≡ exp(− f ). e. when f is holomorphic. ). As for the above deÀnition, it is less arbitrary than may seem at Àrst sight. Indeed, none of the following changes: (i) changing the grid {k/n} to {Const k/n} (ii) changing the lower summation bounds from 0 or 1 to 2,3 .