2 papers
math.DG2011
Focal Rigidity of Flat Tori
Ferry Kwakkel, Marco Martens, Mauricio Peixoto
Given a closed Riemannian manifold (M, g), there is a partition Σ_i of its tangent bundle TM called the focal decomposition. The sets Σ_i are closely associated to focusing of geod…
math.DS2009
An asymptotic universal focal decomposition for non-isochronous potentials
C. A. A. de Carvalho, M. M. Peixoto, D. Pinheiro +1
Galileo, in the XVII century, observed that the small oscillations of a pendulum seem to have constant period. In fact, the Taylor expansion of the period map of the pendulum is co…