— We consider a partially hyperbolic set K on a Riemannian manifold M whose tangent space splits as TKM = E cu⊕Es, for which the centre-unstable direction E expands non-uniformly on some local unstable disk. We show that under these assumptions f induces a Gibbs-Markov structure. Moreover, the decay of the return time function can be controlled in terms of the time typical points need to achiev...

An increasingly popular method of encoding chaotic time-series from physical experiments is the so-called threshold crossings technique, where one simply replaces the real valued data with symbolic data of relative positions to an arbitrary partition at discrete times. The implication has been that this symbolic encoding describes the original dynamical system. On the other hand, the literature...

In the emerging field of network science, a recent model proposes that a hyperbolic geometry underlies the network representation of complex systems, shaping their topology and being responsible for their signature features: scale invariance and strong clustering. Under this model of network formation, points representing system components are placed in a hyperbolic circle and connected if the ...

We consider random products of SL(2,R) matrices that depend on a parameter in non-uniformly hyperbolic regime. show if the dependence is monotone then almost surely product has upper (limsup) Lyapunov exponent equal to value prescribed by Furstenberg Theorem (and hence positive) for all parameters, but lower (liminf) zero dense G? set parameters Hausdorff dimension. As byproduct our methods, we...

We consider random products of SL(2,R) matrices that depend on a parameter in non-uniformly hyperbolic regime. show if the dependence is monotone then almost surely product has upper (limsup) Lyapunov exponent equal to value prescribed by Furstenberg Theorem (and hence positive) for all parameters, but lower (liminf) zero dense Gδ set parameters Hausdorff dimension. As byproduct our methods, we...

Decimating a uniformly sampled signal a factor D involves low-pass antialias filtering with normalized cutoff frequency 1/D followed by picking out every Dth sample. Alternatively, decimation can be done in the frequency domain using the fast Fourier transform (FFT) algorithm, after zero-padding the signal and truncating the FFT. We outline three approaches to decimate nonuniformly sampled sign...