8 edition of **Fuchsian Reduction** found in the catalog.

- 194 Want to read
- 39 Currently reading

Published
**September 18, 2007**
by Birkhäuser Boston
.

Written in English

- Geometry,
- Mathematics,
- Science/Mathematics,
- Applied,
- Differential Equations,
- Geometry - Differential,
- Mathematics / Differential Equations,
- nonlinear differential equations,
- singularity theory

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 289 |

ID Numbers | |

Open Library | OL11388107M |

ISBN 10 | 0817643524 |

ISBN 10 | 9780817643522 |

Fuchsian groups, particularly those which are cocompact, form the tips of several big mathematical icebergs. To put this less metaphorically, several discoveries about Fuchsian groups, obtained using hyperbolic geometry, led to generalizations which fueled the growth of combinatorial and geometric group theory in the 20th century. (mathematics) Any discrete group of isometries of the hyperbolic plane.

Fuchsian functions are described on wikipedia (1) Can anyone state, in a form suitable for reduction to a computer algorithm, a solution or family of solutions of the general equation of degree n (whether based on Fuchsian functions or not)? I had prepared notes on this topic sometime ago so here goes! About this Title: Fuchsian reduction is a method for representing solutions of nonlinear PDEs near singularities. The technique has multiple applications including soliton theory, Einstein's equations and cosmology, stellar models, laser collapse, conformal geometry and combustion. Developed in the s for semilinear wave.

Fuchsia definition is - any of a genus (Fuchsia) of ornamental shrubs of the evening-primrose family having showy nodding flowers usually in deep pinks, reds, and purples. the theory of Fuchsian groups; the material of these lectures is mostly an adaptation from my book “Fuchsian groups” [13]. Lecture III describes the geodesic ﬂow on the surfaces of constant negative curvature and establishes its dynamical properties. Lecture IV is devoted to continued fractions and their relation to coding of Size: 2MB.

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“Fuchsian reduction is an analytical method to represent solutions to non-linear PDEs near singularities. The book under review provides a careful and instructive introduction into this method.

At the end of most of the chapters some problems are posed, which are solved in an by: Fuchsian reduction is a method for representing solutions of nonlinear PDEs near singularities.

The technique has multiple applications including soliton theory, Einstein's equations and cosmology, stellar models, laser collapse, conformal geometry and combustion.

A second-order Fuchsian equation with singular points is completely determined by specifying the values of the characteristic exponents at these points if and only if.

Using a Möbius transformation the equation can be reduced to the form: a), ; b), (the Euler equation); c) —. The Hardcover of the Fuchsian Reduction: Applications to Geometry, Cosmology and Mathematical Physics Fuchsian Reduction book Satyanad Kichenassamy at Barnes & Noble. FREE.

Due to COVID, orders may be delayed. Thank you for your patience. Book Annex Membership. Get this from a library. Fuchsian reduction: applications to geometry, cosmology and mathematical physics. [Satyanad Kichenassamy] -- "This work unfolds systematically in four parts, interweaving theory and applications.

The case studies examined in Part III illustrate the impact of reduction techniques, and may serve as prototypes.

Fuchsian groups on the upper half-plane. Let H = {z in C: Im(z) > 0} be the upper H is a model of the hyperbolic plane when endowed with the metric = +. The group PSL(2,R) acts on H by linear fractional transformations (also known as Möbius transformations): ⋅ = + +.This action is faithful, and in fact PSL(2,R) is isomorphic to the group of all orientation-preserving.

About this Item: Forgotten Books, United States, Paperback. Condition: New. Language: English. Brand new Book. Excerpt from Automorphic Forms and Poincare Series for Infinitely Generated Fuchsian Groups This report represents results obtained at the Courant Institute of Na tical Sciences, New York University, with the United States Army Research Office, Contract No.

Da-aro-(d)u-gis6. Arithmetic Fuchsian groups are a special class of Fuchsian groups constructed using orders in quaternion are particular instances of arithmetic prototypical example of an arithmetic Fuchsian group is the modular group ().They, and the hyperbolic surface associated to their action on the hyperbolic plane often exhibit particularly regular behaviour among Fuchsian groups.

Reduction Theory for Fuchsian Groups Svetlana Katok Department of Mathematics, University of California, Los Angeles, CA, USA 0. Introduction Let F be any Fuchsian group, i.e., a discrete subgroup of the group of isometries of the hyperbolic plane H 2. We consider the unit disc D. Buy Fuchsian Reduction by Satyanad Kichenassamy from Waterstones today.

Click and Collect from your local Waterstones or get FREE UK delivery on orders over £ Cite this chapter as: Kichenassamy S. () Convergent Series Solutions of Fuchsian Initial-Value Problems. In: Fuchsian Reduction. Progress in Nonlinear Author: Satyanad Kichenassamy.

Fuchsian reduction.- Theory of Fuchsian Partial Differential Equation.- Applications.- References.- Index. Fuchsian Groups book. Read reviews from world’s largest community for readers. This introductory text provides a thoroughly modern treatment of Fuchsian /5(7).

Fuchsian Reduction: Applications to Geometry, Cosmology and Mathematical Physics This four-part text beautifully interweaves theory and applications in Fuchsian reduction.

Most chapters contain a problem section and notes with references to the literature. This volume can be used as a text in graduate courses or as a resource for researchers.

holds. In every Fuchsian group there is a subgroup of finite index that has no elements of finite order. The quotient space is compactified by adding a finite number of points corresponding to the improper vertices of a fundamental polygon. There is a unique complex structure on the compactified space for which the quotient mapping is holomorphic.

Here is a Riemann surface of genus, and is. A reduction point algorithm for cocompact Fuchsian groups and applications Article (PDF Available) in Advances in Mathematics of Communications 8(2) May with 71 Reads. In the present article we propose a reduction point algorithm for any Fuchsian group in the absence of parabolic transformations.

We extend to this setting classical algorithms for Fuchsian groups. describe a reduction process that removes parts of the book of I-bundles that cannot intersect a closed quasi-Fuchsian surface. We state and prove the negative case of the main theoremFile Size: 1MB.

Book Book Series. Previous chapter. Next chapter. Chapter Fuchsian Reduction of Differential Equations Chapter Fuchsian Reduction of Differential Equations. In Painlevé Equations and Related Topics: Proceedings of the International Conference, Saint Petersburg, Russia, June 17.

Discover Book Depository's huge selection of Satyanad Kichenassamy books online. Free delivery worldwide on over 20 million titles. We use cookies to give you the best possible experience. Fuchsian Reduction. Satyanad Kichenassamy.

15 Oct Hardback. US$ US$ Save US$ Add to basket. 9% off. Nonlinear Wave Equations. Fuchsian reduction is a method for representing solutions of nonlinear PDEs near singularities.

The technique has multiple applications including soliton theory, Einstein's equations and cosmology, stellar models, laser collapse, conformal geometry and combustion.5/5(2).Chapter III is devoted to Fuchsian-type singular differential equations. For researchers and graduate students interested in differential equations and integral transforms.

This book can also be recommended as a graduate text for students of mathematics and engineering. Category: Mathematics. "Mathematical Analysis does contain a substantial amount of material that is unusual in terms of an introductory text in real analysis These are all interesting topics that have gained increasing importance in modern applications of mathematics, albeit outside the traditional area of analysis.

It is very nice to have these topics developed Author: Mariano Giaquinta.