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Jul 2 |
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On the Complete integrability of a tangent distribution
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Jul 2 |
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On the Complete integrability of a tangent distribution
Dear Robert Bryant, thanks very much for your attention. If I had wait a moment before to post the question, perhaps I could have remembered of the Darboux' reduction theorem in your lectures or of the equivalent Propositions 5.1.2-3 in Foundations of Mechanics by A&M, but I have preferred to get an occasion to communicate with others on the subject I try to learn. Thank you once again. |
Jul 2 |
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On the Complete integrability of a tangent distribution
Dear Jordan Watts, thank you for the reference. Sure it works well and, by the way, hints a proof as the one that initially I have thought. |
Jul 2 |
asked | On the Complete integrability of a tangent distribution |
Jun 28 |
revised |
antiderivative involving modified bessel function
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Jun 28 |
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reference for Noether's theorem
As a starting point you could look at the first volume of Modern Geometry: Methods and applications, by Dubrovin, Fomenko and Novikov |
Jun 28 |
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Non-standard addition theorem for Legendre function of the first kind
Dear Fedor Petrov, I have added the classical analysis tag, thinking it could be useful. |
Jun 28 |
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Non-standard addition theorem for Legendre function of the first kind
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Jun 28 |
answered | What does the word “symplectic” mean? |
Jun 25 |
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symplectic form with partition on unity
corrected an error ; added 1 characters in body |
Jun 25 |
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symplectic form with partition on unity
@Qiaochu Yuan: Sure, you are right, I need to edit lightly the answer. Thank you very much. |
Jun 25 |
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symplectic form with partition on unity
Dear Daniel Pomerleano, excuse me, but, if $\omega$ is a symplectic form on a compact connected manifold $M$, should not its cohomology class be necessarily nonzero? infact $[\omega]=0$ imply $[\omega^n]=[\omega]^n=0$ and this last contradicts $\int_M\omega\neq 0$. Bye. |
Jun 25 |
answered | symplectic form with partition on unity |
Jun 24 |
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What's difference between 'functional' and 'function'?
I think this definition is also somewhere in Lang's Linear Algebra. |
Jun 23 |
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On degenerate integrable hamiltonian systems
Dear Daniele Sepe, thanks for your reference. In this paper the integrability condition of Mischenko and Fomenko is interpreted as sufficient for the existence of an isotropic and symplectically complete fibration (FISC after Dazord and Delzant) and hence of generalized action-angle coordinates. I learn also that the first use of the notion of FISC in concrete examples of mechanical interest is the book Nonlinear Poisson Bracket of Maslov and Karasev, and the other paper of Fassò on Euler-Poinsot that you cite. Thank you. |
Jun 23 |
accepted | On degenerate integrable hamiltonian systems |
Jun 23 |
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On degenerate integrable hamiltonian systems
Dear jvkersch, thank you for the reference. Even if in this book there is no mention of degenerate (or super, non commutative) integrability, the detailed analysis of the topology of the momentum map for many classical ham. systems ( Euler top, kepler problem, harmonic oscillator,...; that, by the way, are superintegrable) should permit to recognize the existence of generalized action-angle coordinates at least on a open subset of the phase space. |
Jun 21 |
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On degenerate integrable hamiltonian systems
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Jun 21 |
asked | On degenerate integrable hamiltonian systems |
Jun 19 |
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The fibers of the momentum map for the $SO(n+1)$ symmetry of the geodesic flow on $S^n$
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