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Remarks on the systoles of symmetric convex hypersurfaces and symplectic capacities
In this note we study the systoles of convex hypersurfaces in R2n invariant under an anti-symplectic involution. We investigate a uniform upper bound...
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Singular dynamics under a weak potential on a sphere
We give a detailed analytical description of the global dynamics of a point mass moving on a sphere under the action of a logarithmic potential. We...
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On Implicit ODEs with Hexagonal Web of Solutions
Solutions of an implicit ODE form a web. Already for a cubic ODE the 3-web of solutions has a nontrivial local invariant, namely the curvature form....
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A symmetry of sphere map implies its chaos*
A well-known example, given by Shub, shows that for any | d | ≥ 2 there is a self-map of the sphere S n , n ≥ 2, of degree d for which the set of...