48 citations · 134 across the 20 of their papers we have counts for
9 papers · 1 filter
KAM splittings and equidistributed periodic orbits for stable hypersurfaces
Robert Cardona, Oliver Edtmair, Rohil Prasad
We show that any stable hypersurface of a symplectic -manifold, on which the cohomology class of the symplectic form restricts to a multiple of a rational class, can be $C^\inft…
Stability is not open or generic in symplectic four-manifolds
Robert Cardona
Given an embedded stable hypersurface in a four-dimensional symplectic manifold, we prove that it is stable isotopic to a -close stable hypersurface with the following propert…
An -principle for embeddings transverse to a contact structure
Robert Cardona, Francisco Presas
Given a class of embeddings into a contact or a symplectic manifold, we give a sufficient condition, that we call isocontact or isosymplectic realization, for this class to satisfy…
Existence and classification of -contact structures
Robert Cardona, Cédric Oms
A -contact structure on a -manifold is a Jacobi structure on satisfying a transversality condition along the hypersurface . We show that, in three dimensions,…
Morse functions and contact convex surfaces
Robert Cardona, Cédric Oms
Let be a Morse function on a closed surface such that zero is a regular value and such that admits neither positive minima nor negative maxima. In this expository note,…
Integrable systems on singular symplectic manifolds: From local to global
Robert Cardona, Eva Miranda
In this article we consider integrable systems on manifolds endowed with singular symplectic structures of order one. These structures are symplectic away from an hypersurface wher…
Euler flows and singular geometric structures
Robert Cardona, Eva Miranda, Daniel Peralta-Salas
Tichler proved that a manifold admitting a smooth closed one-form fibers over a circle. More generally a manifold admitting independent closed one-forms fibers over a torus $T^…
On the volume elements of a manifold with transverse zeroes
Robert Cardona, Eva Miranda
Moser proved in 1965 in his seminal paper that two volume forms on a compact manifold can be conjugated by a diffeomorphism, that is to say they are equivalent, if and only if thei…
Integrable systems and closed one forms
Robert Cardona, Eva Miranda
In the first part of this paper we revisit a classical topological theorem by Tischler (1970) and deduce a topological result about compact manifolds admitting a set of independent…