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C2 densely the 2-sphere has an elliptic closed geodesic

Published online by Cambridge University Press:  18 October 2004

GONZALO CONTRERAS and
FERNANDO OLIVEIRA
GONZALO CONTRERAS
Affiliation:
CIMAT, PO Box 402, 36.000 Guanajuato, GTO, Mexico (e-mail: gonzalo@cimat.mx)
FERNANDO OLIVEIRA
Affiliation:
Departamento de Matematica, Instituto de Ciencias Exatas, Univesidade Federal de Minas Gerais, Av. Antonio Carlos 6627, Caixa Postal 702, 30161-970 Belo Horizonte MG, Brazil (e-mail: fernando@mat.ufmg.br)
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Abstract

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We prove that a Riemannian metric on the 2-sphere or the projective plane can be C2 approximated by a $C^\infty$ metric whose geodesic flow has an elliptic closed geodesic.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 5 , October 2004, pp. 1395 - 1423
Copyright
© 2004 Cambridge University Press