Hello frNdZz!! ...... I recently came across a important branch of studying dynamic systems .... ERGODIC THEORY .... I had started with some pdf from the internet but they're too complex so I need ya guys to help me out.....

**HOW DO I START**. ..... Can someone guide me through the pre requisite material required ?....

kindly reply 😊

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TopNewestHow about this one? I think it's a nice introduction, explaining ergodic theory from a mathematical standpoint, and then later progresses to applications in dynamical systems.

Ergodic Theory

I agree with you, almost everywhere you look, ergodic theory gets real dense right off at the start, requiring much more than basic skills in calculus. – Michael Mendrin · 2 years, 2 months ago

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– Abhinav Raichur · 2 years, 2 months ago

I went through a few pages.... I think I can grasp it 😃... Thanks.... But it is still not clear as to what ergodic th contains... What are your views on it 😐?Log in to reply

– Michael Mendrin · 2 years, 2 months ago

Can you restate your question more clearly?Log in to reply

if you were my teacher how would you tell me to approach it.– Abhinav Raichur · 2 years, 2 months agoLog in to reply

As an example, we could imagine, say, a complicated planetary system, which, in spite of Isaac Newton's idealization of it as some kind of beautiful and precise "clockwork", is in fact slightly chaotic. Suppose we plot all of its possible states in some configuration space. We would have a kind of a volume or a cloud in that configuration space, which, in fact, over a very long period of time, can change and evolve over time. Ergodic theory attempts to analyze the behavior of this cloud over time. Many other examples exists in chaotic theory, where something seemingly random isn't totally random---patterns show up when states are plotted, and we see "strange attractors" , i.e., unexpected structures when we'd normally be expecting featureless scatterplots. It's a difficult field of study, but after a while you get the idea that nothing is truly as random as you think. It's really hard to achieve perfect randomness---some order is happening, if you know where to find it, and that order evolves over time. – Michael Mendrin · 2 years, 2 months ago

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(at least the elementary stuff).... Thank you very much for taking all the time in writing this .....* you gave me the best gift on my birthday* !!!! – Abhinav Raichur · 2 years, 2 months agoLog in to reply