Timeline for Question about theorem in Arnold's book on action-angles variables

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Sep 13, 2015 at 12:04	history	edited	QuantumTheory	CC BY-SA 3.0	added 227 characters in body
Sep 12, 2015 at 23:02	comment	added	QuantumTheory		@ChrisGerig mhmm, I don't think I fully understand. Do you mind turning this into a complete answer and explain what you exactly use there?- I agree that we know that $(I,\phi)$ are coordinates, as for fixed $I$ we define $M_f$ and $M_f$ is nothing but a torus, which we can then parametrize via the angle variables. Thus, if we have another type of coordinates on $M_f$ (for instance your $q$ variables, then this would be okay, but I currently don't see what you mean).
Sep 12, 2015 at 22:43	comment	added	Chris Gerig		The Inverse Function Theorem will give coordinates $(0,q)$ on $M_f\subset \mathbb{R}^{2n}$. We also know that $(I,\phi)$ are the coordinates for the neighborhood of $M_f$ (in $\mathbb{R}^{2n}$). That's what Arnold is using.
Sep 12, 2015 at 20:16	history	edited	QuantumTheory	CC BY-SA 3.0	added 483 characters in body
Sep 12, 2015 at 20:08	comment	added	QuantumTheory		@ChrisGerig Could you elaborate? Just to clarify this, the question is not why $M_f$ is a manifold (reg. value theorem), but why we can take $(I,q)$ as (apparently even global) coordinates in the nbh. of $M_f$?
Sep 12, 2015 at 20:00	history	edited	QuantumTheory	CC BY-SA 3.0	added 188 characters in body
Sep 12, 2015 at 14:11	history	edited	QuantumTheory	CC BY-SA 3.0	added 23 characters in body
Sep 12, 2015 at 13:56	history	asked	QuantumTheory	CC BY-SA 3.0