15 citations · 31 across the 8 of their papers we have counts for
9 papers
Multiple reductions, foliations and the dynamics of cluster maps
Inês Cruz, Helena Mena-Matos, M. Esmeralda Sousa-Dias
Presymplectic and Poisson reduction of cluster maps are described in terms of the "canonical" foliations of presymplectic and Poisson manifolds. This approach to reduction leads to…
Dynamics and periodicity in a family of cluster maps
Inês Cruz, Helena Mena-Matos, M. Esmeralda Sousa-Dias
The dynamics of a 1-parameter family of cluster maps associated to mutation-periodic quivers in dimension 4, is studied in detail. The use of presymplectic reduction leads to…
Dynamics of the birational maps arising from and quivers
Inês Cruz, Helena Mena-Matos, M. Esmeralda Sousa-Dias
The dynamics of the maps associated to and quivers is studied in detail. We show that the corresponding reduced symplectic maps are conjugate to globally periodic maps…
Discrete dynamical systems from mutation-periodic quivers: examples and reduction
Inês Cruz, M. Esmeralda Sousa-Dias
Several new mutation-periodic quivers of period higher than 1 are introduced as well as the associated discrete dynamical systems. The reduction of these systems is developed using…
Reduction of cluster iteration maps to symplectic maps
Inês Cruz, M. Esmeralda Sousa-Dias
We study iteration maps of recurrence relations arising from mutation periodic quivers of arbitrary period. Combining tools from cluster algebra theory and (pre)symplectic geometry…
A unified framework for the computation of polynomial quadrature weights and errors
Mário M. Graça, M. Esmeralda Sousa-Dias
For the class of polynomial quadrature rules we show that conveniently chosen bases allow to compute both the weights and the theoretical error expression of a -point rule via t…
Nonlinear Stability of Riemann Ellipsoids with Symmetric Configurations
Miguel Rodriguez-Olmos, M. Esmeralda Sousa-Dias
We apply geometric techniques to obtain the necessary and sufficient conditions on the existence and nonlinear stability of self-gravitating Riemann ellipsoids having at least two…
The fundamental group of -manifolds
L. Godinho, M. E. Sousa-Dias
We address the problem of computing the fundamental group of a symplectic -manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compac…
The Symplectic Normal Space of a Cotangent-Lifted Action
Matthew Perlmutter, Miguel Rodriguez-Olmos, M. Esmeralda Sousa-Dias
For the cotangent bundle of a smooth Riemannian manifold acted upon by the lift of a smooth and proper action by isometries of a Lie group, we characterize the symplectic normal sp…