Stable ergodicity and physical measures for weakly hyperbolic dynamical systems

(a) The easiest thing to do is to apply the algorithm from the lecture: take the matrix (A | I) and bring it to the reduced row echelon form; for an invertible matrix A, the result

Namely, differential privacy, secure multi-party computation, homomorphic encryption, federated learning, secure enclaves, and automatic data de-identification.. We will briefly

Namely, differential privacy, secure multi-party computation, homomorphic encryption, federated learning, secure enclaves, and automatic data de-identification.. We will briefly

For large classes of dynamical systems with good mixing properties, it is possible to obtain strong statistical limit laws such as the central limit theorems and its

The pool of examples of partially hyperbolic diffeomor- phisms is larger than that of Anosov diffeomorphisms, in particular, due to the fact that extensions (e.g. F ×id N ) of

(Recall that S~(z) does not contain the origin 0.) In this subsection, we introduce quantities that measure the multiplicity of such tangencies and then

When the vector field Z is holomorphic the real vector fields X and Y (cf. This follows from a straightforward computation in local coordinates.. Restriction to the

In our previous paper [CY], by using the varia- tional method, we have shown that the diffusion orbits exist in generic a priori unstable time-periodic Hamiltonian systems with