Eva Miranda

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1,609 appearances 1 recordings 1 series first heard Jan 2025 last heard Jan 2025

Eva Miranda’s voice in public audio — every appearance, attributed to the second.

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I'm going to take an holomorphic function on C two.

Okay?

And I'm going to decompose it as its real and imaginary part.

Tis well known?

that uh this real and imaginary part of holomorphic function, they follow the Cauchy-Riemann equations.

The Cauchy-Roman equations can be written as as as here.

Okay.

These are some relations between the real and imaginary part.

And indeed, something that it's very, very surprising is that this is the same as saying that H and G defines an integrable system.

This is this is mind blowing, okay?

For which Poisson bracket?

Well you take omega zero and omega one.

just the real and imaginary part of this of this uh deset deset one, desert two.

It's an integral system with respect

to two brackets.

So it's super interesting.

So Considerman equations can be seen as an equation of integrable system.

So now

I want to understand because I I want to use these integrable systems to explain me how to pair position and momentum.

And I'm I'm taking here an example.

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