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Periodic Differential Equations in the Plane: A Topological Perspective, Rafael Ortega


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Автор: Rafael Ortega
Название:  Periodic Differential Equations in the Plane: A Topological Perspective
ISBN: 9783110550405
Издательство: Walter de Gruyter
Классификация:



ISBN-10: 3110550407
Обложка/Формат: Hardcover
Страницы: 195
Вес: 0.46 кг.
Дата издания: 06.05.2019
Серия: Mathematics
Язык: English
Размер: 244 x 170 x 13
Читательская аудитория: Professional and scholarly
Ключевые слова: Differential calculus & equations,Analytic topology,Geometry, MATHEMATICS / Geometry / General,MATHEMATICS / Differential Equations / General,MATHEMATICS / Topology
Поставляется из: Германии
Описание: Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effects. The most traditional approach to study these equations is based on the introduction of small parameters, but the search of nonlocal results leads to the application of several topological tools. Examples are fixed point theorems, degree theory, or bifurcation theory. These well-known methods are valid for equations of arbitrary dimension and they are mainly employed to prove the existence of periodic solutions. Following the approach initiated by Massera, this book presents some more delicate techniques whose validity is restricted to two dimensions. These typically produce additional dynamical information such as the instability of periodic solutions, the convergence of all solutions to periodic solutions, or connections between the number of harmonic and subharmonic solutions. The qualitative study of periodic planar equations leads naturally to a class of discrete dynamical systems generated by homeomorphisms or embeddings of the plane. To study these maps, Brouwer introduced the notion of a translation arc, somehow mimicking the notion of an orbit in continuous dynamical systems. The study of the properties of these translation arcs is full of intuition and often leads to non-rigorous proofs. In the book, complete proofs following ideas developed by Brown are presented and the final conclusion is the Arc Translation Lemma, a counterpart of the Poincare–Bendixson theorem for discrete dynamical systems. Applications to differential equations and discussions on the topology of the plane are the two themes that alternate throughout the five chapters of the book.

Differential Equations and Linear Algebra

Автор: Strang
Название: Differential Equations and Linear Algebra
ISBN: 0980232791 ISBN-13(EAN): 9780980232790
Издательство: Cambridge Academ
Рейтинг:
Цена: 60180.00 T
Наличие на складе: Невозможна поставка.
Описание: Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.

Periodic Solutions of First-Order Functional Differential Equations in Population Dynamics

Автор: Seshadev Padhi; John R. Graef; P. D. N. Srinivasu
Название: Periodic Solutions of First-Order Functional Differential Equations in Population Dynamics
ISBN: 8132218949 ISBN-13(EAN): 9788132218944
Издательство: Springer
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Цена: 83850.00 T
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Описание: Periodic Solutions of First-Order Functional Differential Equations in Population Dynamics

Periodic Solutions of First-Order Functional Differential Equations in Population Dynamics

Автор: Seshadev Padhi; John R. Graef; P. D. N. Srinivasu
Название: Periodic Solutions of First-Order Functional Differential Equations in Population Dynamics
ISBN: 8132235428 ISBN-13(EAN): 9788132235422
Издательство: Springer
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Цена: 88500.00 T
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Описание: Chapter 1. Introduction.- Chapter 2. Positive Periodic Solutions of Nonlinear Functional Differential Equations with Parameter λ.- Chapter 3. Multiple Periodic Solutions of a System of Functional Differential Equations.- Chapter 4. Multiple Periodic Solutions of Nonlinear Functional Differential Equations.- Chapter 5. Asymptotic Behavior of Periodic Solutions of Differential Equations of First Order.- Bibliography.

Partial differential equations: time-periodic solutions

Автор: Otto Vejvoda; L. Herrmann; V. Lovicar; M. Sova; I.
Название: Partial differential equations: time-periodic solutions
ISBN: 9024727723 ISBN-13(EAN): 9789024727728
Издательство: Springer
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Цена: 231990.00 T
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Extended States for the Schrodinger Operator with Quasi-Periodic Potential in Dimension Two

Автор: Yulia Karpeshina, Roman Shterenberg
Название: Extended States for the Schrodinger Operator with Quasi-Periodic Potential in Dimension Two
ISBN: 1470435438 ISBN-13(EAN): 9781470435431
Издательство: Mare Nostrum (Eurospan)
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Цена: 83160.00 T
Наличие на складе: Невозможна поставка.
Описание: Considers a Schrodinger operator $H=-\Delta +V(\vec x)$ in dimension two with a quasi-periodic potential $V(\vec x)$. The authors prove that the absolutely continuous spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties.

Almost Periodic and Almost Automorphic Solutions to Integro-Differential Equations

Автор: Marko Kostic
Название: Almost Periodic and Almost Automorphic Solutions to Integro-Differential Equations
ISBN: 3110641240 ISBN-13(EAN): 9783110641240
Издательство: Walter de Gruyter
Цена: 140030.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book discusses almost periodic and almost automorphic solutions to abstract integro-differential Volterra equations that are degenerate in time, and in particular equations whose solutions are governed by (degenerate) solution operator families with removable singularities at zero. It particularly covers abstract fractional equations and inclusions with multivalued linear operators as well as abstract fractional semilinear Cauchy problems.

Quasi-periodic Standing Wave Solutions of Gravity-Capillary Water Waves

Автор: Massimiliano Berti, Riccardo Montalto
Название: Quasi-periodic Standing Wave Solutions of Gravity-Capillary Water Waves
ISBN: 1470440695 ISBN-13(EAN): 9781470440695
Издательство: Mare Nostrum (Eurospan)
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Цена: 71060.00 T
Наличие на складе: Нет в наличии.
Описание: The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable $x$) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.

Spherical and Plane Integral Operators for PDEs: Construction, Analysis, and Applications

Автор: Karl K. Sabelfeld, Irina A. Shalimova
Название: Spherical and Plane Integral Operators for PDEs: Construction, Analysis, and Applications
ISBN: 3110315297 ISBN-13(EAN): 9783110315295
Издательство: Walter de Gruyter
Рейтинг:
Цена: 185890.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.

Textbook on Ordinary Differential Equations

Автор: Ahmad Shair
Название: Textbook on Ordinary Differential Equations
ISBN: 3319164074 ISBN-13(EAN): 9783319164076
Издательство: Springer
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Цена: 46570.00 T
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Описание: The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics. A complete Solutions Manual, containing solutions to all the exercises published in the book, is available.

Differential Equations, Dynamical Systems, and an Introduction to Chaos

Автор: Morris W. Hirsch
Название: Differential Equations, Dynamical Systems, and an Introduction to Chaos
ISBN: 0123820103 ISBN-13(EAN): 9780123820105
Издательство: Elsevier Science
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Цена: 88690.00 T
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Описание: Suitable for students in the fields of mathematics, science, and engineering, this title provides a theoretical approach to dynamical systems and chaos. It helps them to analyze the types of differential equations that arise in their area of study.

Differentiable Dynamical Systems

Автор: Wen Lan
Название: Differentiable Dynamical Systems
ISBN: 1470427990 ISBN-13(EAN): 9781470427993
Издательство: Mare Nostrum (Eurospan)
Рейтинг:
Цена: 112860.00 T
Наличие на складе: Невозможна поставка.
Описание: This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the Ω-stability theorem of Smale.While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study.

Topological Optimization and Optimal Transport: In the Applied Sciences

Автор: Maitine Bergounioux, ?douard Oudet, Martin Rumpf,
Название: Topological Optimization and Optimal Transport: In the Applied Sciences
ISBN: 3110439263 ISBN-13(EAN): 9783110439267
Издательство: Walter de Gruyter
Рейтинг:
Цена: 173490.00 T
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Описание:

By discussing topics such as shape representations, relaxation theory and optimal transport, trends and synergies of mathematical tools required for optimization of geometry and topology of shapes are explored. Furthermore, applications in science and engineering, including economics, social sciences, biology, physics and image processing are covered.

Contents
Part I

  • Geometric issues in PDE problems related to the infinity Laplace operator
  • Solution of free boundary problems in the presence of geometric uncertainties
  • Distributed and boundary control problems for the semidiscrete Cahn-Hilliard/Navier-Stokes system with nonsmooth Ginzburg-Landau energies
  • High-order topological expansions for Helmholtz problems in 2D
  • On a new phase field model for the approximation of interfacial energies of multiphase systems
  • Optimization of eigenvalues and eigenmodes by using the adjoint method
  • Discrete varifolds and surface approximation

Part II

  • Weak Monge-Ampere solutions of the semi-discrete optimal transportation problem
  • Optimal transportation theory with repulsive costs
  • Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations
  • On the Lagrangian branched transport model and the equivalence with its Eulerian formulation
  • On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows
  • Pressureless Euler equations with maximal density constraint: a time-splitting scheme
  • Convergence of a fully discrete variational scheme for a thin-film equatio
  • Interpretation of finite volume discretization schemes for the Fokker-Planck equation as gradient flows for the discrete Wasserstein distance


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