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  • Dynamics of Partial Differential Equations

    Series series Mathematics and Statistics (R0)
    This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently.Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions ... Read more

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    Classical Methods and Recent Advances

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    The book investigates classical and more recent methods of study for the asymptotic behavior of dissipative continuous dynamical systems with applications to ordinary and partial differential equations, the main question being convergence (or not) of the solutions to an equilibrium. After reviewing the basic concepts of topological dynamics and the definition of gradient-like systems on a metric ... Read more

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  • Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

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    Series series Mathematics and Statistics (R0)
    These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity ... Read more

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  • Dynamical Systems with Applications using MATLAB®

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    This textbook, now in its second edition, provides a broad introduction to both continuous and discrete dynamical systems, the theory of which is motivated by examples from a wide range of disciplines. It emphasizes applications and simulation utilizing MATLAB®, Simulink®, the Image Processing Toolbox® and the Symbolic Math toolbox®, including MuPAD.Features new to the second edition include· ... Read more

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  • Difference Equations, Discrete Dynamical Systems and Applications

    ICDEA, Wuhan, China, July 21-25, 2014

    Series series Springer Nature Proceedings excluding Computer Science
    These proceedings of the 20th International Conference on Difference Equations and Applications cover the areas of difference equations, discrete dynamical systems, fractal geometry, difference equations and biomedical models, and discrete models in the natural sciences, social sciences and engineering.The conference was held at the Wuhan Institute of Physics and Mathematics, Chinese Academy of ... Read more

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  • Hamiltonian Partial Differential Equations and Applications

    Series Book 75 - Fields Institute Communications
    This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to ... Read more

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  • Multiple Time Scale Dynamics

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    This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a ... Read more

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  • A Short Course in Ordinary Differential Equations

    by Qingkai Kong ...
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    This text is a rigorous treatment of the basic qualitative theory of ordinary differential equations, at the beginning graduate level. Designed as a flexible one-semester course but offering enough material for two semesters, A Short Course covers core topics such as initial value problems, linear differential equations, Lyapunov stability, dynamical systems and the Poincaré—Bendixson theorem, and ... Read more

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  • Mathematical Challenges in a New Phase of Materials Science

    Kyoto, Japan, August 2014

    Series series Springer Nature Proceedings excluding Computer Science
    This volume comprises eight papers delivered at the RIMS International Conference "Mathematical Challenges in a New Phase of Materials Science", Kyoto, August 4–8, 2014. The contributions address subjects in defect dynamics, negatively curved carbon crystal, topological analysis of di-block copolymers, persistence modules, and fracture dynamics. These papers highlight the strong interaction ... Read more

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  • Patterns of Dynamics

    Berlin, July 2016

    Series series Springer Nature Proceedings excluding Computer Science
    Theoretical advances in dynamical-systems theory and their applications to pattern-forming processes in the sciences and engineering are discussed in this volume that resulted from the conference Patterns in Dynamics held in honor of Bernold Fiedler, in Berlin, July 25-29, 2016.The contributions build and develop mathematical techniques, and use mathematical approaches for prediction and control ... Read more

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    Using phase–plane analysis, findings from the theory of topological horseshoes and linked-twist maps, this book presents a novel method to prove the existence of chaotic dynamics. In dynamical systems, complex behavior in a map can be indicated by showing the existence of a Smale-horseshoe-like structure, either for the map itself or its iterates. This usually requires some assumptions about the ... Read more

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  • Bifurcation Theory of Functional Differential Equations

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    This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and ... Read more

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