Why is there no self in the container of the 5 aggregates? I can see that there is no self to find in the 5 aggregates. But what about their container ? 

I have a recurrent thought which troubles me : I imagine the 5 aggregates happening within a frame, which is a different one for every living creature. 

There is this frame, this perspective, which is unique for any of us, starts at birth, and ends at death. The five aggregates can only be experienced through that perspective. 

I can't feel what my cat is feeling when I touch it, I can only experience the aggregates appearing inside my perspective, not the one of the cat.

I don't feel like this is contradicting any buddhist view. The problem is that I don't see how one is suppose not to identify with his own perspective. 

1) Where is the impermanence in this ?

2) How can identifying a self there can lead to suffering ?

3) Is there a reference about it in the suttas ?
This is the problem with mixing up ultimate reality with conventional reality. In ultimate reality, the cat does not exist. What is real is the tactile experience of the touch. That experience is an instance of the 5 aggregates arising due to causes. The experience is impermanent, unsatisfactory and non-self.

'Container' is only a concept in the mind. It doesn't exist. Sights can be sensed, sounds can be sensed, aromas can be sensed, tastes can be sensed, tactile sensations can be sensed, mental objects can be sensed. 'Container' is not something that can be sensed. So it's nothing more than a concept. It has no basis in ultimate reality. Vipassana meditation is about stop looking at the world in terms of entities and start looking at the world in terms of experiences. You cannot see the 3 characteristics in concepts.