An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds

For a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m ≥ 4, we provide an algorithm for estimating the values of the topological invariant Dm r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing Dm r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63–84]. An open-source implementation of the algorithm programmed in C++ is publicly available at http://www.pawelpilarczyk.com/combtop/.

Conflito e trauma: XVI Colóquio de Outono

It has been the main concern of CEHUM, as a Research Centre within the Humanities which operates in an inter and transdisciplinary structure to listen attentively to the “noise of the world” and attempt a global interpretation of the signs of the times issuing from the world around us, as vibrant echoes of many social and cultural pressing issues. Every year each new Colóquio de Outono attempts to give evidence of that concern through the topic chosen for debate, ample enough and challenging enough to trigger a lively multidisciplinary dialogue amongst the diff erent research groups that compose this centre, the participants and our invited guest speakers. Throughout the three days of this 16th Colóquio de Outono we had the privilege to debate the propositions of a vast number of national and international specialists in the manifold fi elds of inquiry here represented, engaging keynote speakers, project advisors, members of research teams and external researchers attached to the various research projects currently running in CEHUM, in the fi elds of literature, linguistics, philosophy, ethics, visual arts, cultural studies, music and performance. Each specifi c fi eld of studies was however never seen isolated, but always embodied in a geo-cultural context and within the scope of a wide variety of critical debates and current theories of knowledge, as a signal of our understanding of the Humanities as a rich and plural territory which engages us all, scholars, researchers, students.