Topological Invariants of Plane Curves and Caustics (University Lecture Series) Book PDF, ePub eBook

Join our eBook service for unlimited books & audiobooks. Get a free 7 day subscription! ↓↓↓↓↓


Book Descriptions:
This book describes recent progress in the topological study of plane curves. The theory of plane curves is much richer than knot theory, which may be considered the commutative version of the theory of plane curves. This study is based on singularity theory: the infinite-dimensional space of curves is subdivided by the discriminant hypersurfaces into parts consisting of generic curves of the same type. The invariants distinguishing the types are defined by their jumps at the crossings of these hypersurfaces. Arnold describes applications to the geometry of caustics and of wavefronts in symplectic and contact geometry. These applications extend the classical four-vertex theorem of elementary plane geometry to estimates on the minimal number of cusps necessary for the reversion of a wavefront and to generalizations of the last geometrical theorem of Jacobi on conjugated points on convex surfaces. These estimates open a new chapter in symplectic and contact topology: the theory of Lagrangian and Legendrian collapses, providing an unusual and far-reaching higher-dimensional extension of Sturm theory of the oscillations of linear combinations of eigenfunctions.

Topological Invariants of Plane Curves and Caustics (University Lecture Series) by V. I. Arnold

From reader reviews:

Patricia Welling:

Now a day individuals who Living in the era wherever everything reachable by talk with the internet and the resources inside can be true or not require people to be aware of each info they get. How many people to be smart in acquiring any information nowadays? Of course the reply is reading a book. Looking at a book can help men and women out of this uncertainty Information particularly this Topological Invariants of Plane Curves and Caustics (University Lecture Series) book because book offers you rich data and knowledge. Of course the details in this book hundred percent guarantees there is no doubt in it as you know.

Jose Tiernan:

This Topological Invariants of Plane Curves and Caustics (University Lecture Series) are reliable for you who want to certainly be a successful person, why. The key reason why of this Topological Invariants of Plane Curves and Caustics (University Lecture Series) can be among the great books you must have will be giving you more than just simple studying food but feed anyone with information that maybe will shock your before knowledge. This book will be handy, you can bring it everywhere and whenever your conditions in the e-book and printed versions. Beside that this Topological Invariants of Plane Curves and Caustics (University Lecture Series) forcing you to have an enormous of experience such as rich vocabulary, giving you test of critical thinking that we realize it useful in your day task. So , let's have it and revel in reading.

Cecilia Moore:

The reserve with title Topological Invariants of Plane Curves and Caustics (University Lecture Series) contains a lot of information that you can learn it. You can get a lot of profit after read this book. That book exist new knowledge the information that exist in this e-book represented the condition of the world today. That is important to yo7u to understand how the improvement of the world. This specific book will bring you in new era of the globalization. You can read the e-book on the smart phone, so you can read the item anywhere you want.

Brant Castillo:

People live in this new morning of lifestyle always make an effort to and must have the free time or they will get great deal of stress from both way of life and work. So , once we ask do people have extra time, we will say absolutely indeed. People is human not really a huge robot. Then we question again, what kind of activity are there when the spare time coming to anyone of course your answer will unlimited right. Then do you try this one, reading publications. It can be your alternative with spending your spare time, the actual book you have read is usually Topological Invariants of Plane Curves and Caustics (University Lecture Series).