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Carathéodory balls and norm balls in H p , n = z n : z p < 1

Binyamin Schwarz, Uri Srebro (1996)

Banach Center Publications

It is shown that for n ≥ 2 and p > 2, where p is not an even integer, the only balls in the Carathéodory distance on H p , n = z n : z p < 1 which are balls with respect to the complex l p norm in n are those centered at the origin.

Chaos in D0 brane dynamics

I. Aref'eva, P. Medvedev, O. Rytchkov, I. Volovich (1998)

Banach Center Publications

We consider the classical and quantum dynamics of D0 branes within the Yang-Mills approximation. Using a simple ansatz we show that a classical trajectory exhibits a chaotic motion. Chaotic dynamics in N=2 supersymmetric Yang-Mills theory is also discussed.

Characterization of diffeomorphisms that are symplectomorphisms

Stanisław Janeczko, Zbigniew Jelonek (2009)

Fundamenta Mathematicae

Let ( X , ω X ) and ( Y , ω Y ) be compact symplectic manifolds (resp. symplectic manifolds) of dimension 2n > 2. Fix 0 < s < n (resp. 0 < k ≤ n) and assume that a diffeomorphism Φ : X → Y maps all 2s-dimensional symplectic submanifolds of X to symplectic submanifolds of Y (resp. all isotropic k-dimensional tori of X to isotropic tori of Y). We prove that in both cases Φ is a conformal symplectomorphism, i.e., there is a constant c ≠0 such that Φ * ω Y = c ω X .

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