Download PDF by Igor Nikolaev (auth.): Foliations on Surfaces

By Igor Nikolaev (auth.)

Foliations is among the significant techniques of contemporary geometry and topology which means a partition of topological house right into a disjoint sum of leaves. This e-book is dedicated to geometry and topology of floor foliations and their hyperlinks to ergodic idea, dynamical platforms, complicated research, differential and noncommutative geometry. This finished publication addresses graduate scholars and researchers and should function a reference publication for specialists within the field.

Show description

Read or Download Foliations on Surfaces PDF

Best combinatorics books

Paul-Hermann Zieschang's Theory of Association Schemes PDF

This e-book is a concept-oriented remedy of the constitution idea of organization schemes. The generalization of Sylow’s team theoretic theorems to scheme thought arises by reason of arithmetical issues approximately quotient schemes. the idea of Coxeter schemes (equivalent to the speculation of structures) emerges obviously and yields a simply algebraic evidence of titties’ major theorem on constructions of round kind.

Download e-book for iPad: Lectures in Geometric Combinatorics (Student Mathematical by Rekha R. Thomas

This publication offers a path within the geometry of convex polytopes in arbitrary measurement, appropriate for a complicated undergraduate or starting graduate pupil. The booklet begins with the fundamentals of polytope idea. Schlegel and Gale diagrams are brought as geometric instruments to imagine polytopes in excessive measurement and to unearth extraordinary phenomena in polytopes.

New PDF release: Combinatorics : an introduction

Bridges combinatorics and chance and uniquely comprises precise formulation and proofs to advertise mathematical thinkingCombinatorics: An creation introduces readers to counting combinatorics, bargains examples that function particular ways and ideas, and provides case-by-case equipment for fixing difficulties.

Additional info for Foliations on Surfaces

Example text

We see at once how 42 2. Morse-Smale Foliations to extend the homeomorphism h to M*\8M* via the equation hetz = (thz, where z E 8V U {qi}. 1 One easily sees that h is invertible (the mapping h- 1 can be constructed in the same manner, replacing by (). It remains to prove that h is continuous. Our proof is much the same as in [234J. The continuity of h is evident at sinks, sources and in the neighbourhoods of saddles and saddle elements. We shall prove the continuity of h at the points of stable separatrices of the saddle elements.

A 'singularity scheme' is the equivalence class of words for a relation E. The following statement, proved in [92], is a sufficient condition of CO-equivalence. 2 (Takens-Dumortier) If(X,L i , Wd and (Y,L 2 , W 2 ) are two triples defined as above, and if they have the same 'singularity scheme', Wi rv W 2 , different from the word C;:, then there exists a homeomorphism h from the neighbourhood U of the singularity X(O) of the vector field X to the neighbourhood V of the singularity Y(O) of the vector field Y which conjugates the orbits of X and Y near 0, preserving their orientation.

19) takes the form ~~ = -X1/ + D2x 3, ~~ dB 2 dt = -B + B = -1/ + 1/ 2 - D2X21/ + D2B4 y 2 - 2 C 2By , dy dt + C2X21/ 4; 3 = -By + C 2y . 20). Ml is an elementary point (not hyperbolic) and is a topological node when D2 < 0, and a topological saddle when D2 > O. The point M2 is a hyperbolic saddle. 21) is an elementary point with one eigenvalue equal to zero. This is a node if C2 < 0 and a saddle if C2 > O. 19) is unfolded, and it is a weak (ii)-singularity when D2 > 0, C 2 > 0; a weak (i)-singularity when D 2C 2 < 0; and a weak (iii)-singularity when D2 < 0, C 2 < O.

Download PDF sample

Rated 4.41 of 5 – based on 46 votes