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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 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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3. 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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4. Berkovich Spaces and Applications
edited by Antoine Ducros, Charles Favre, Johannes Nicaise
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2015
シリーズ名: Lecture Notes in Mathematics ; 2119
オンライン: http://dx.doi.org/10.1007/978-3-319-11029-5
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Introduction to Berkovich analytic spaces
Etale cohomology of schemes and analytic spaces
Countability properties of Berkovich spaces
Cohomological finiteness of proper morphisms in algebraic geometry: a purely transcendental proof, without projective tools
Bruhat-Tits buildings and analytic geometry
Dynamics on Berkovich spaces in low dimensions
Compactifications of spaces of representations (after Culler, Morgan and Shalen)
Introduction to Berkovich analytic spaces
Etale cohomology of schemes and analytic spaces
Countability properties of Berkovich spaces
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5. Evolutionary Equations with Applications in Natural Sciences
edited by Jacek Banasiak, Mustapha Mokhtar-Kharroubi
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2015
シリーズ名: Lecture Notes in Mathematics ; 2126
オンライン: http://dx.doi.org/10.1007/978-3-319-11322-7
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Wilson Lamb: Applying functional analytic techniques to evolution equations
Adam Bobrowski: Boundary conditions in evolutionary equations in biology.-Ernesto Estrada: Introduction to Complex Networks: Structure and Dynamics.-Jacek Banasiak: Kinetic models in natural sciences
Philippe Laurençot: Weak compactness techniques and coagulation equations
Ryszard Rudnicki: Stochastic operators and semigroups and their applications in physics and biology
Mustapha Mokhtar-Kharroubi: Spectral theory for neutron transport.-Anna Marciniak-Czochra: Reaction-diffusion-ODE models of pattern formation
Mapundi Kondwani Banda: Nonlinear Hyperbolic Systems of Conservation Laws and Related Applications
Wilson Lamb: Applying functional analytic techniques to evolution equations
Adam Bobrowski: Boundary conditions in evolutionary equations in biology.-Ernesto Estrada: Introduction to Complex Networks: Structure and Dynamics.-Jacek Banasiak: Kinetic models in natural sciences
Philippe Laurençot: Weak compactness techniques and coagulation equations
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6. Quantum Quadratic Operators and Processes. 1st ed. 2015
by Farrukh Mukhamedov, Nasir Ganikhodjaev
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2015
シリーズ名: Lecture Notes in Mathematics ; 2133
オンライン: http://dx.doi.org/10.1007/978-3-319-22837-2
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Introduction
Quadratic Stochastic Operators
Quadratic Processes
Analytic methods in the theory of quadratic stochastic processes
Quantum quadratic operators
Quantum quadratic operators on M2(C)
Infinite-dimensional quadratic operators
Quantum quadratic stochastic processes
Introduction
Quadratic Stochastic Operators
Quadratic Processes
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7. Twisted Teichmüller Curves
by Christian Weiß
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2014
シリーズ名: Lecture Notes in Mathematics ; 2104
オンライン: http://dx.doi.org/10.1007/978-3-319-04075-2
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Introduction
Background
Teichmüller Curves
Twisted Teichmüller Curves
Stabilizer and Maximality
Calculations for Twisted Teichmüller Curves
Prym Varieties and Teichmüller Curves
Lyapunov Exponents
Kobayashi Curves Revisited
Appendix
Tables
List of Symbols
Index
Bibliography
Introduction
Background
Teichmüller Curves
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8. 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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9. The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
by Arnaud Debussche, Michael Högele, Peter Imkeller
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2013
シリーズ名: Lecture Notes in Mathematics ; 2085
オンライン: http://dx.doi.org/10.1007/978-3-319-00828-8
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Introduction
The fine dynamics of the Chafee- Infante equation
The stochastic Chafee- Infante equation
The small deviation of the small noise solution
Asymptotic exit times
Asymptotic transition times
Localization and metastability
The source of stochastic models in conceptual climate dynamics
Introduction
The fine dynamics of the Chafee- Infante equation
The stochastic Chafee- Infante equation
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10. Invariance Entropy for Deterministic Control Systems : An Introduction
by Christoph Kawan
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2013
シリーズ名: Lecture Notes in Mathematics ; 2089
オンライン: http://dx.doi.org/10.1007/978-3-319-01288-9
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Basic Properties of Control Systems
Introduction to Invariance Entropy
Linear and Bilinear Systems
General Estimates
Controllability, Lyapunov Exponents, and Upper Bounds
Escape Rates and Lower Bounds
Examples
Notation
Bibliography
Index
Basic Properties of Control Systems
Introduction to Invariance Entropy
Linear and Bilinear Systems