Discipline: Mathematiques

and help). I am grateful to all these institutions. This has been a long trip and many people have of course been there sharing the journey. All of them should know my deep gratitude. However, I wish to express explicit acknowledgement to some of the persons which were specially important for the project itself. Both Sylvain Crovisier and Mart́ın Sambarino, my advisors, were of course very important and even essential in this project. I want to thank Sylvain for his infinite patience and dedication, he has clearly dedicated more time to this project than it is expected and this has had an important effect on its results, I want to profit to express my great admiration to him as a brilliant mathematician and as a person: He is incredibly generous, humble and kind, and even if sometimes it is hard to get strength to speak to someone which is so good, he makes you feel always comfortable and he is always encouraging, I could never even try to list all what I learned from him. Mart́ın has been my advisor and friend since the very start of my studies, he has been my window to mathematics and he has always been open to pursue wit