48 citations · 134 across the 20 of their papers we have counts for
21 papers
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…
Algebraic and Geometric Models for Space Networking
William Bernardoni, Robert Cardona, Jacob Cleveland +6
In this paper we introduce some new algebraic and geometric perspectives on networked space communications. Our main contribution is a novel definition of a time-varying graph (TVG…
Hydrodynamic and symbolic models of computation with advice
Robert Cardona
Dynamical systems and physical models defined on idealized continuous phase spaces are known to exhibit non-computable phenomena, examples include the wave equation, recurrent neur…
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,…
Periodic orbits and Birkhoff sections of stable Hamiltonian structures
Robert Cardona, Ana Rechtman
Stable Hamiltonian structures generalize contact forms and define a volume-preserving vector field known as the Reeb vector field. We study two aspects of Reeb vector fields define…
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,…
The Universal -Metric on Merge Trees
Robert Cardona, Justin Curry, Tung Lam +1
Adapting a definition given by Bjerkevik and Lesnick for multiparameter persistence modules, we introduce an -type extension of the interleaving distance on merge trees. We…
Looking at Euler flows through a contact mirror: Universality and undecidability
Robert Cardona, Eva Miranda, Daniel Peralta-Salas
The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. In recent papers [5, 6, 7, 8] several unknown facets of the E…
Turing universality of the incompressible Euler equations and a conjecture of Moore
Robert Cardona, Eva Miranda, Daniel Peralta-Salas
In this article we construct a compact Riemannian manifold of high dimension on which the time dependent Euler equations are Turing complete. More precisely, the halting of any Tur…
The periodic orbit conjecture for steady Euler flows
Robert Cardona
The periodic orbit conjecture states that, on closed manifolds, the set of lengths of the orbits of a non-vanishing vector field all whose orbits are closed admits an upper bound.…
Constructing Turing complete Euler flows in dimension
Robert Cardona, Eva Miranda, Daniel Peralta-Salas +1
Can every physical system simulate any Turing machine? This is a classical problem which is intimately connected with the undecidability of certain physical phenomena. Concerning f…
Path Optimization Sheaves
Michael Moy, Robert Cardona, Robert Green +3
Motivated by efforts to incorporate sheaves into networking, we seek to reinterpret pathfinding algorithms in terms of cellular sheaves, using Dijkstra's algorithm as an example. W…
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…
The topology of Bott integrable fluids
Robert Cardona
We construct non-vanishing steady solutions to the Euler equations (for some metric) with analytic Bernoulli function in each three-manifold where they can exist: graph manifolds.…
Steady Euler flows and Beltrami fields in high dimensions
Robert Cardona
Using open books, we prove the existence of a non-vanishing steady solution to the Euler equations for some metric in every homotopy class of non-vanishing vector fields of any odd…
Universality of Euler flows and flexibility of Reeb embeddings
Robert Cardona, Eva Miranda, Daniel Peralta-Salas +1
The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao launched a programme to address the global exis…
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…