Category Archives: Dynamical system

A dynamical proof of Fermat’s little theorem

If you have studied number theory (even just a little bit), you should know the Fermat’s little theorem: for any positive , and for any prime number , we have . Here I will give a proof by using a … Continue reading

Posted in Dynamical system, Number Theory | 3 Comments

Poincaré recurrence theorem and its friends

The Poincaré recurrence theorem states that a dynamical system (under suitable conditions) will eventually return to a condition that is very close to the original condition. Slightly more formally, for a compact set in , if is a volume preserving … Continue reading

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A meta post, and two articles

1. Is there any way to support MathJax here? It can translate directly the latex code to display math. It is supported on blogspot, I find it more convenient. 2. I believe many of us come across some very good articles … Continue reading

Posted in Dynamical system, Uncategorized | 2 Comments

A dynamical proof of some Diophantine approximations

Diophantine approximations is a field in number theory which asks how good a real number can be approximated by some rational number. Quite a number of classical results are proved by using combinatorics, which is not friendly to people who … Continue reading

Posted in Dynamical system, Number Theory | 2 Comments