This is an expository paper devoted to the Morse index of Chaperon’s generating families of Hamiltonian diffeomorphisms. After reviewing the construction of such generating families, we present Bott’s iteration theory in this setting: we study how the Morse index of a critical point corresponding to an iterated periodic orbit depends on the order of iteration of the orbit. We also investigate t...

Large datasets describing geometric shapes are nowadays available in a variety of applications, including Geographical Information System. Handling such shapes require extensive computing resources. One of the most computer-intensive task is the analysis of their morphological structure. Morse Theory is a powerful theory, that is used to address the problem of describing topology, i.e., the sha...

Terrain visualization has been an interesting issue for graphics people for long, and there have been a lot of attempts in various ways for more e cient visualization. In most of the works the terrain data was considered as a triangular mesh as it is, or as an implicit surface in which the original shape(topology) of the terrain can be slightly changed. Recently, the Morse Theory, [1, 2], has b...