Project in Dynamical system and chaos.

The idea of the project is:

Choose a topic that you can explain by these materials

1-one-dimentional map
2- Two-dimensional map
3-choas in one dimensional.
4-Fractals
5-chaos in 2-Dimenion
6-Strange attractors
7-Diffrential equations

You have to search for examples and proof that will support your topic.

You can NOT copy the examples and proof you need to just take the idea of the examples and proof and then rewrite it by your way.

you need to provide example or proof for each concept.

Also, you need to write Abstract and Introduction for this topic.

Also, You need to use graphs for your result.

Finally, You have to write conclusion of this project and the references.

Also, you need to write it in mathematical notation.

You should try to be a creative with the material.

Please read the instructions in the two pages

from 10 - 12 pages

In this project you are asked to generate an overview of all the important concepts, facts, told techniques you have learned this semester.

"Fixed points" of this project:

- All chapters that we covered this setn.ter have to be included.

- Connections between chapters need to be made.

- You need to provide at least one example/proof that supports each concept or fact you consider (for example for stability of orbits you only need one example/proof either in 1D or more dimensions. but you can have more than one for sure: same for LyE, or fractal dimension, or itineraries, or differential equations, etc.). Overall, your final has to contain at least four solid proofs/examples.

You 1 most likely need more than four.

Now, here's the catch: these examples/proofs cannot be from your book or the notes. Consider this the research part of the project. Include the references for your examples if you use any. Of course you cannot just copy examples from somewhere else! You need to put in your own thoughts and work. Finding your own original examples is another good approach!

- Theoretic, results need to be supplemented/complemented by numerical investigations using the computer. Use it, of the programs you have seen or created this seilitt5ter.

- Use complete sentences and correct mathematical notation. Imagine you have to explain chaos to somebody who knows nothing about it, but who has a fair mathematical maturity.

- Project structure (resembling a journal paper): 1. Title/author and affiliation