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1. Divergent Series, Summability and Resurgence I : Monodromy and Resurgence
by Claude Mitschi, David Sauzin
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2016
シリーズ名: Lecture Notes in Mathematics ; 2153
オンライン: http://dx.doi.org/10.1007/978-3-319-28736-2
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Preface.-Preface to the three volumes
Part I:Monodromy in Linear Differential Equations
1 analytic continuation and monodromy
Differential Galois Theory
Inverse Problems
The Riemann-Hilbert problem
Part II: Introduction to 1-Summability and Resurgence
5 Borel-Laplace Summation
Resurgent Functions and Alien Calculus
the Resurgent Viewpoint on Holomorphic Tangent-to-Identity Germs
Acknowledgements
Index
Preface.-Preface to the three volumes
Part I:Monodromy in Linear Differential Equations
1 analytic continuation and monodromy
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2. Divergent Series, Summability and Resurgence III : Resurgent Methods and the First Painlevé Equation
by Eric Delabaere
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2016
シリーズ名: Lecture Notes in Mathematics ; 2155
オンライン: http://dx.doi.org/10.1007/978-3-319-29000-3
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Avant-Propos
Preface to the three volumes
Preface to this volume
Some elements about ordinary differential equations
The first Painlevé equation
Tritruncated solutions for the first Painlevé equation
A step beyond Borel-Laplace summability
Transseries and formal integral for the first Painlevé equation
Truncated solutions for the first Painlevé equation
Supplements to resurgence theory
Resurgent structure for the first Painlevé equation
Index
Avant-Propos
Preface to the three volumes
Preface to this volume
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3. Divergent Series, Summability and Resurgence II : Simple and Multiple Summability
by Michèle Loday-Richaud
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2016
シリーズ名: Lecture Notes in Mathematics ; 2154
オンライン: http://dx.doi.org/10.1007/978-3-319-29075-1
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Avant-propos
Preface to the three volumes
Introduction to this volume
1 Asymptotic Expansions in the Complex Domain
2 Sheaves and Čech cohomology
3 Linear Ordinary Differential Equations
4 Irregularity and Gevrey Index Theorems
5 Four Equivalent Approaches to k-Summability
6 Tangent-to-Identity Diffeomorphisms
7 Six Equivalent Approaches to Multisummability
Exercises
Solutions to Exercises
Index
Glossary of Notations
References
Avant-propos
Preface to the three volumes
Introduction to this volume
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4. Nonlinear Water Waves : Cetraro, Italy 2013
by Adrian Constantin, Joachim Escher, Robin Stanley Johnson, Gabriele Villari ; edited by Adrian Constantin
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2016
シリーズ名: Lecture Notes in Mathematics ; 2158
オンライン: http://dx.doi.org/10.1007/978-3-319-31462-4
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Adrian Constantin: Exact travelling periodic water waves in two-dimensional irrotational flows
Joachim Escher: Breaking Water Waves
Robin Stanley Johnson: Asymptotic methods for weakly nonlinear and other water waves
Gabriele Villari: A survival kit in phase plane analysis: some basic models and problems
Adrian Constantin: Exact travelling periodic water waves in two-dimensional irrotational flows
Joachim Escher: Breaking Water Waves
Robin Stanley Johnson: Asymptotic methods for weakly nonlinear and other water waves
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5. Bifurcation without Parameters
by Stefan Liebscher
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2015
シリーズ名: Lecture Notes in Mathematics ; 2117
オンライン: http://dx.doi.org/10.1007/978-3-319-10777-6
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Introduction
Methods & Concepts
Cosymmetries
Codimension One
Transcritical Bifurcation
Poincar´e-Andronov-Hopf Bifurcation
Application: Decoupling in Networks
Application: Oscillatory Profiles
Codimension Two
egenerate Transcritical Bifurcation
egenerate Andronov-Hopf Bifurcation
Bogdanov-Takens Bifurcation
Zero-Hopf Bifurcation
Double-Hopf Bifurcation
Application: Cosmological Models
Application: Planar Fluid Flow
Beyond Codimension Two
Codimension-One Manifolds of Equilibria
Summary & Outlook
Introduction
Methods & Concepts
Cosymmetries
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6. Mathematical Models of Viscous Friction
by Paolo Buttà, Guido Cavallaro, Carlo Marchioro
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2015
シリーズ名: Lecture Notes in Mathematics ; 2135
オンライン: http://dx.doi.org/10.1007/978-3-319-14759-8
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1.  Introduction
2. Gas of point particles
3. Vlasov approximation
4. Motion of a body immersed in a Vlasov system
5. Motion of a body immersed in a Stokes fluid
A Infinite Dynamics
1.  Introduction
2. Gas of point particles
3. Vlasov approximation
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7. Asymptotic Integration of Differential and Difference Equations
by Sigrun Bodine, Donald A. Lutz
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2015
シリーズ名: Lecture Notes in Mathematics ; 2129
オンライン: http://dx.doi.org/10.1007/978-3-319-18248-3
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Introduction, Notation, and Background
Asymptotic Integration for Differential Systems
Asymptotics for Solutions of Difference Systems
Conditioning Transformations for Differential Systems
Conditioning Transformations for Difference Systems
Perturbations of Jordan Differential Systems
Perturbations of Jordan Difference Systems
Applications to Classes of Scalar Linear Differential Equations
Applications to Classes of Scalar Linear Difference Equations
Asymptotics for Dynamic Equations on Time Scales
Introduction, Notation, and Background
Asymptotic Integration for Differential Systems
Asymptotics for Solutions of Difference Systems
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8. Current Challenges in Stability Issues for Numerical Differential Equations : Cetraro, Italy 2011, Editors: Luca Dieci, Nicola Guglielmi
by Wolf-Jürgen Beyn, Luca Dieci, Nicola Guglielmi, Ernst Hairer, Jesús María Sanz-Serna, Marino Zennaro
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2014
シリーズ名: Lecture Notes in Mathematics ; 2082
オンライン: http://dx.doi.org/10.1007/978-3-319-01300-8
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Studies on current challenges in stability issues for numerical differential equations
Long-Term Stability of Symmetric Partitioned Linear Multistep Methods
Markov Chain Monte Carlo and Numerical Differential Equations
Stability and Computation of Dynamic Patterns in PDEs
Continuous Decompositions and Coalescing Eigen values for Matrices Depending on Parameters
Stability of linear problems: joint spectral radius of sets of matrices
Studies on current challenges in stability issues for numerical differential equations
Long-Term Stability of Symmetric Partitioned Linear Multistep Methods
Markov Chain Monte Carlo and Numerical Differential Equations
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9. Singular Perturbations : Introduction to System Order Reduction Methods with Applications
by Elena Shchepakina, Vladimir Sobolev, Michael P. Mortell
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2014
シリーズ名: Lecture Notes in Mathematics ; 2114
オンライン: http://dx.doi.org/10.1007/978-3-319-09570-7
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Introduction
Slow Integral Manifolds
The Book of Numbers
Representations of Slow Integral Manifolds
Singular Singularly Perturbed Systems
Reduction Methods for Chemical Systems
Specific Cases
Canards and Black Swans
Appendix: Proofs
Introduction
Slow Integral Manifolds
The Book of Numbers
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10. Introduction to Stokes Structures
by Claude Sabbah
出版情報: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013
シリーズ名: Lecture Notes in Mathematics ; 2060
オンライン: http://dx.doi.org/10.1007/978-3-642-31695-1
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