3 citations · 4 across the 5 of their papers we have counts for
9 papers
The topology of the monodromy map of the second order ODE
Dan Burghelea, Nicolau C. Saldanha, Carlos Tomei
We consider the following question: given , which potentials for the second order Sturm-Liouville problem have as its Floquet multiplier? More precisely, def…
The topology of critical sets of some ordinary differential operators
Nicolau C. Saldanha, Carlos Tomei
We survey recent work of Burghelea, Malta and both authors on the topology of critical sets of nonlinear ordinary differential operators. For a generic nonlinearity , the critic…
Stability of compact actions of the Heisenberg group
Tania M. Begazo, Nicolau C. Saldanha
Let G be the Heisenberg group of real lower triangular 3x3 matrices with unit diagonal. A locally free smooth action of G on a manifold M^4 is given by linearly independent vector…
Homotopy and cohomology of spaces of locally convex curves in the sphere
Nicolau C. Saldanha
We discuss the homotopy type and the cohomology of spaces of locally convex parametrized curves gamma: [0,1] -> S^2, i.e., curves with positive geodesic curvature. The space of all…
Nilpotent pseudogroups of functions on an interval
Tania M. Begazo, Nicolau C. Saldanha
A near-identity nilpotent pseudogroup of order m >= 1 is a family f_1, ..., f_n: (-1,1) -> R of C^2 functions for which: |f_i - id|_{C^1} < epsilon for some small positive real num…
Results on infinite dimensional topology and applications to the structure of the critical set of nonlinear Sturm-Liouville operators
Dan Burghelea, Nicolau C. Saldanha, Carlos Tomei
We consider the nonlinear Sturm-Liouville differential operator for , a Sobolev space of functions satisfying Dirichlet boundary condition…