Finding a Book on Manifolds: Definitions and More

In summary, the conversation is about finding a book that includes definitions for the terms "manifold," "stable manifold," and "unstable manifold." The suggested book for reference is S.N. Chow and J. Hale's "Methods of bifurcation theory," published by Springer in 1982. A link to the book is not provided, but it can be found in stores and libraries.
  • #1
thepioneerm
33
0
Please:

I need abook that include this Definitions:

1- Manifold

2- Stable Manifold

3- unstable Manifold



thank you.
 
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  • #2
S.N. Chow and J. Hale: Methods of bifurcation theory. Springer, 1982

http://en.wikipedia.org/wiki/Stable_manifold" [Broken]
 
Last edited by a moderator:
  • #3
yyat said:
S.N. Chow and J. Hale: Methods of bifurcation theory. Springer, 1982

http://en.wikipedia.org/wiki/Stable_manifold" [Broken]

thank very much :)

but do you have the link of this book ?!
 
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  • #4
thepioneerm said:
thank very much :)

but do you have the link of this book ?!

I don't know if the full text is online, but you can find the book in stores and libraries:

http://books.google.com/books?id=on3YAAAACAAJ&dq=chow+hale+methods+of+bifurcation+theory&ei=hWLCScjCBJCsyASvxb3VBA" [Broken]
 
Last edited by a moderator:
  • #5
thank very very much :) :)
 

1. What is a manifold?

A manifold is a mathematical concept that describes a space that is locally Euclidean, meaning it looks like a flat plane when zoomed in, but may have a more complex curvature when viewed from a larger perspective. In other words, a manifold is a higher-dimensional surface that can be smoothly bent and twisted without tearing or stretching.

2. Why is it important to understand manifolds?

Manifolds play a crucial role in many areas of mathematics and science, particularly in geometry, topology, and physics. They are used to model and study complex systems and phenomena, such as the structure of the universe, the behavior of particles in space, and the shape of biological molecules.

3. Can you explain the concept of dimensionality in relation to manifolds?

Dimensionality refers to the number of independent coordinates needed to describe a point in a space. In the case of manifolds, the dimensionality is the number of parameters needed to specify a position on the surface. For example, a two-dimensional manifold, such as a sphere, requires two coordinates (latitude and longitude) to locate a point, while a three-dimensional manifold, such as a torus, requires three coordinates (x, y, and z) to locate a point.

4. How is a manifold different from a surface or a space?

A manifold can be thought of as a generalization of both surfaces and spaces. While surfaces are two-dimensional and spaces are three-dimensional, manifolds can have any number of dimensions. Additionally, manifolds have a smooth and continuous structure, unlike surfaces which can have abrupt changes or corners, and spaces which can have singularities or discontinuities.

5. Are there any real-world applications of manifolds?

Yes, there are many real-world applications of manifolds, including in computer graphics, computer vision, machine learning, and data analysis. For example, manifolds can be used to model and analyze complex data sets, such as images, sounds, or text, allowing for efficient and accurate processing and classification.

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