By Daniel Bertrand, Benjamin Enriquez, Claude Mitschi, Claude Sabbah, and Reinhard Schäfke
This specific quantity is devoted to the reminiscence of Andrey A. Bolibrukh. It includes expository articles dedicated to a few elements of Bolibrukh's paintings, via ten refereed study articles. themes disguise advanced linear and nonlinear differential equations and quantum teams: monodromy, Fuchsian linear platforms, Riemann-Hilbert challenge, differential Galois concept, differential algebraic teams, multisummability, isomonodromy, PainlevÃ© equations, Schlesinger equations, integrable platforms, KZ equations, advanced mirrored image teams, and root platforms. A e-book of the eu Mathematical Society. dispensed in the Americas via the yankee Mathematical Society.
Read Online or Download Differential Equations and Quantum Groups: Andrey A. Bolibrukh Memorial Volume PDF
Best differential equations books
This e-book covers the entire crucial subject matters on differential equations, together with sequence strategies, Laplace transforms, platforms of equations, numerical equipment and part airplane equipment. transparent factors are precise with many present examples.
This moment version of a hugely winning graduate textual content provides an entire creation to partial differential equations and numerical research. Revised to incorporate new sections on finite quantity equipment, converted equation research, and multigrid and conjugate gradient equipment, the second one version brings the reader up to date with the newest theoretical and business advancements.
Multigrid provides either an basic creation to multigrid tools for fixing partial differential equations and a modern survey of complicated multigrid innovations and real-life purposes. Multigrid tools are valuable to researchers in clinical disciplines together with physics, chemistry, meteorology, fluid and continuum mechanics, geology, biology, and all engineering disciplines.
During this booklet, the fundamental equipment of nonlinear research are emphasised and illustrated in basic examples. each thought of process is encouraged, defined in a normal shape yet within the easiest attainable summary framework. Its functions are proven, fairly to boundary price difficulties for undemanding usual or partial differential equations.
- Partial Differential Equations in Action: From Modelling to Theory (Universitext)
- Equazioni a derivate parziali: Metodi, modelli e applicazioni
- Non-Linear Partial Differential Equati0Ns
- Existence of global solutions of elliptic systems
- Stability, instability and chaos. An introduction to the theory of nonlinear differential equations
Additional resources for Differential Equations and Quantum Groups: Andrey A. Bolibrukh Memorial Volume
The additional case is the Goryachev–Chaplygin case, where, only on the manifold W0 (that is, for 2 = 0), K = r(p2 + q 2 ) + pγ3 is a first integral. The fact that the three and half mentioned cases are the only ones in which the system has an algebraic additional integral has been proved by Husson . With a meromorphic first integral, it has been proved by Ziglin  using techniques which were invented by him  and are close to the ones I want to discuss here, namely properties of the monodromy groups of the (linearized) differential system.
Hence the Hénon–Heiles system is not Liouville integrable (at least with a rational first integral). I like this example very much, because this is really a beautiful academic example. Firstly, I have given two completely different arguments for the seemingly different properties (K) and (L). Secondly, it shows that the Galois group is something very rich. Of course, it contains the monodromy group of the variational equation, and hence also its Zariski closure. But, in this simple example, the Riemann surface is simply connected so that there is no monodromy at all.
29 29 31 32 34 34 35 36 37 38 39 40 41 42 43 44 46 46 I remember Andrei sitting in my office in Strasbourg and telling me his admiration for Sofia Kowalevskaya. I am not sure whether this was because I am a woman, or because he knew I had written a long paper on the “Kowalevski top”  or simply 28 Michèle Audin because he was very enthusiastic over her brilliant and romantic personality. I would have been very happy to discuss the topic of the present paper with him. It is with deep sadness, thinking both of Sofia and Andrei, that I reproduce (in Figure 1), the very first page of the beautiful paper  on the rigid body.