A dinâmica topológica de inversões geométricas foi estudada em . O espa ̧co de parâmetros das medidas de Markov com suporte no atrator do sistema é um aberto de R3 folheado por superfícies de nível compactas definidas pela entropia métrica: superfícies isentrópicas . Neste artigo abordaremos o aspecto geométrico dessas superfícies. Em particular, classificaremos suas geodésicas e pontos umbílicos.
Research about recommendation systems has increased due to the amount of information that it is available to individuals. In the music context these systems help the individual to filter and discover new songs according the individual's taste. Most of the business music companies use a recommendation system, based on the characteristics of a song listened by an individual, but a group recommendation system is still underexplored. For a shared environment when there is music, the songs selection will be more efficient if a group recommendation system is used. The goal of this project is to develop a music recommendation for a group that, is sharing the same environment, taking into consideration the context. For this reason, in this work we will employ the Spotify API to recover the data of playlists that were listened by an individual, collecting its preferences and adding them to the others individuals playlists.