INJECTIVITY AS A TRANSVERSALITY PHENOMENON IN GEOMETRIES OF NEGATIVE CURVATURE

摘要

The global asymptotic stability conjecture in dynamical systems was solved recently and independently by Feller, Glutsiuk and Gutierrez. Crucial to the approach of Gutierrez is the folowing theorem ofhis:A local diffeomorphism f:R~2 -> R~2 for which the eigenvalues of D f(x) miss (0,∞) must be injective .The present paper gives a partial generalization of this theorem to local diffeomorphisms between Hadamard surfaces, the spectral condition being replace by transversality conditions among certain foliations associated to horocycles. The proofs use arguments from global analysis.