4 citations · 6 across the 4 of their papers we have counts for
5 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…