Does uniform hyperbolicity requires both or any of the stable and unstable spaces?

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Consider the bernoulli shift map,

From the definition in this article in scholarpedia,

We say that f is uniformly hyperbolic or an Anosov diffeomorphism if for every x∈M there is a splitting of the tangent space $T_xM=E^s(x)⊕E^u(x)$

The question is weather the definition of uniformly hyperbolic system requires the splitting of the tangent space to have both stable and unstable spaces, or if it can just contain the unstable space (e.g. the case of the Bernoulli shift).

My understanding is that it is hyperbolic if the dimension of the centered space is 0, which supports the idea that it does not required both spaces, but the definition in the article seems to be ambiguous in that respect. The definition in the book of Ott is also inconclusive to this discussion.

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It depends on whether you are interested in an invertible dynamical system or not. If you have only (strong) expanding directions, for example you can hardly get something invertible.

But of course you can condier maps like $x\to 2 x (\mod 1)$ on the circle and call it hyperbolic (and chaotic).