Arnold Mathematical Journal Volume 1 Issue 1

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Journal Description Arnold Mathematical Journal

2015 Arnold Mathematical Journal

doi:10.1007/s40598-015-0006-6

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Periods of Pseudo-Integrable Billiards

Dragović, Vladimir; Radnović, Milena

2015 Arnold Mathematical Journal

doi:10.1007/s40598-014-0004-0

Consider billiard desks composed of two concentric half-circles connected with two edges. We examine billiard trajectories having a fixed circle concentric with the boundary semicircles as the caustic, such that the rotation numbers with respect to the half-circles are $$\rho _1$$ ρ 1 and...

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Classification of Finite Metric Spaces and Combinatorics of Convex Polytopes

Vershik, A.

2015 Arnold Mathematical Journal

doi:10.1007/s40598-014-0005-z

We describe the canonical correspondence between finite metric spaces and symmetric convex polytopes, and formulate the problem about classification of the metric spaces in terms of combinatorial structure of those polytopes.

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Space of Smooth 1-Knots in a 4-Manifold: Is Its Algebraic Topology Sensitive to Smooth Structures?

Viro, Oleg

2015 Arnold Mathematical Journal

doi:10.1007/s40598-015-0007-5

We discuss a possibility to get an invariant of a smooth structure on a closed simply connected 4-manifold from homotopy invariants of the space of loops smoothly embedded into the manifold.

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Problems Around Polynomials: The Good, The Bad and The Ugly...

Shapiro, Boris

2015 Arnold Mathematical Journal

doi:10.1007/s40598-015-0008-4

The Russian style of formulating mathematical problems means that nobody will be able to simplify your formulation as opposed to the French style which means that nobody will be able to generalize it,—Vladimir Arnold.

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Arnold Mathematical Journal Volume 1 Issue 1

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