Toplogy book for study of dynamical systems

In summary, the conversation is about a person looking for a good book on topology and metric spaces due to their lack of pre-knowledge in the subject. They specifically mention wanting a book with a lot of diagrams to aid with visualization. The other person suggests Munkres Topology or searching for basic topology videos on YouTube.
  • #1
sandylam966
12
0
need a good book on topology and metric spaces! I'm an undergrad taking a course on non-linear dynamical systems, just realising my pre-knowledge is slightly under the requirement since I have not taken any course on topology. I only know basic real analysis and some complex analysis.
so any good introduction on topology would be good. In particular, I prefer a lot of diagrams which can help with visaulising the concepts. many thanks in advance!
 
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  • #2
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
  • #3
Well, Munkres Topology is a possibility, but I'm not sure it would be quite what you want. I'm a very visual thinker, but I'm pretty good at generating my own visuals, so I don't always bother to track down the best book for that, especially if it's kind of introductory level stuff. You might want to try youtube. I'm too lazy to track it down, but I think I came across some good basic topology videos. I was only interested in a certain topic, since I already know the subject, so I only saw a couple, myself, but I think there are more out there.
 

Related to Toplogy book for study of dynamical systems

1. What is topology and how does it relate to dynamical systems?

Topology is a branch of mathematics that studies the properties of spaces that are preserved under continuous transformations. It is used in the study of dynamical systems to understand the behavior of systems over time and to identify patterns and structures within them.

2. What are some common applications of topology in the study of dynamical systems?

Topology has a variety of applications in the study of dynamical systems, including modeling biological systems, understanding chaotic behavior in weather patterns, and analyzing the dynamics of financial markets.

3. What are some key concepts that are covered in a topology book for the study of dynamical systems?

Some key concepts that are typically covered in a topology book for the study of dynamical systems include topological spaces, continuity, compactness, and connectedness. These concepts are essential for understanding the behavior of dynamical systems.

4. What are some recommended topology books for the study of dynamical systems?

Some recommended topology books for the study of dynamical systems include "An Introduction to Dynamical Systems" by David Ruelle, "Topology and Dynamical Systems" by Robert Gilmore, and "Chaos and Fractals: New Frontiers of Science" by Heinz-Otto Peitgen, Hartmut Jürgens, and Dietmar Saupe.

5. Is a strong background in mathematics necessary to understand topology and dynamical systems?

While a strong background in mathematics can certainly be helpful in understanding topology and dynamical systems, it is not always necessary. Many topology books for the study of dynamical systems are written for a general audience and do not require advanced mathematical knowledge. However, a basic understanding of calculus and linear algebra is often helpful in understanding the concepts presented in these books.

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