i have a simple 2d circle oscillating on xy plane and i want to apply a texture that will be stretched along with the circle's animation.
(it would be best to do that after the animation at the end of the network)

apply the texture coordinates before the animation.

Also, use a Rest node.

http://www.tokeru.com/cgwiki/index.php?title=Rest_Attrib [www.tokeru.com]

Midphase
Also, use a Rest node.

but then i would have to trasfer the texture to point colors, i will need i high point count to get a decent resolution

You don't need to create point colors if it's for rendering

Imagine simple quad polygon with planar uvs, if you deform afterwards or copy uvs from nondeformed to deformed the applied material textures will appear to deform with it
uvs will be interpolated at rendertime from the corners of the quad and corresponding colors will be sampled from textures.

Your circle is technically an n-gon and principle is exactly the same, uvs will be interpolated within for every sample.
This can obviously create some unwanted artifacts especially when interpolating inside of n-gons as in your example so you may need to ensure your shape is divided and deformed appropriately for whatever result you want to get

tamte
if you deform afterwards or copy uvs from nondeformed to deformed the applied material textures will appear to deform with it

see the image attached, this is how i tried to do it but its not working very well.the texture is being deformed but it is floating a bit..
something confusing to me is that inside the solver im working with lines and points i do not have the circle i started with, as you see i close the curve with an “add” node after. so i dont know exactly how would i go about UVing this.
this is a problem also for dividing the geo after the solver,it gets divided each frame the new points are not deformed.

Use Attribute Copy, not Transfer
If the point numbers are matching it will work fine
If your deformed are just points, maybe copy P from deformed to nondeformed rather than uv the other way