4
$\begingroup$

I would like to know whether the continuity of the stable and unstable subbundles $E^{s}$ and $E^{u}$ follows from the growth conditions as in the discrete case, or must be hypothesized, in the definitions of hyperbolic sets for flows.

$\endgroup$
1
$\begingroup$

Yes, it follows from the growth conditions. It should be done in standard texts (e.g. Katok-Hasselblatt) but I have not checked. Indeed, it is a general fact about dominated splittings.

In fact, the growth conditions provide a gap in the singular values of the map and this forces the existence of a continuous splitting. See for example this paper by Bochi and Gourmelon (see also section 2 of this paper where it is explicitly stated for flows).

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.