Real analytic convex surfaces with positive topological entropy and rigid body dynamics
type: Item
instance of: scholarly article
title: Real analytic convex surfaces with positive topological entropy and rigid body dynamics
zbMATH Open document ID: 0791.58073
DOI: 10.1007/BF02599321
author: Gabriel P. Paternain
published in: Manuscripta Mathematica
publication date: 1994-07-14T00:00:00Z
full work available at URL: https://eudml.org/doc/155816
review text: The author exhibits explicit real analytic metrics on \(S^ 2\) and \(\mathbb{R} P^ 2\) with positive curvature and positive topological entropy. These metrics are constructed from the Euler Poisson flows which describe the motion of a rigid body on axially symmetric face fields. It is shown that for specific force fields the flow possesses a horseshoe and hence positive topological entropy. Via the Maupertuis principle these flows give rise to convex metrics on \(S^ 2\) with positive topological entropy.
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53D25
Mathematics Subject Classification ID: 53C99
Mathematics Subject Classification ID: 54C70
Mathematics Subject Classification ID: 52A15
zbMATH DE Number: 492739
zbMATH Keywords: rigid body dynamics
zbMATH Keywords: topological entropy
zbMATH Keywords: Euler Poisson flows
zbMATH Keywords: convex metrics
MaRDI profile type: Publication
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OpenAlex ID: W1997589832
description: scientific article; zbMATH DE number 492739