Simultaneously non-dense orbits under different expanding maps

Diophantine Approximation by Orbits of Expanding Markov Maps

Given a dynamical system ([0, 1], T ), the distribution properties of the orbits of real numbers x ∈ [0, 1] under T constitute a longstanding problem. In 1995, Hill and Velani introduced the ”shrinking targets” theory, which aims at investigating precisely the Hausdorff dimensions of sets whose orbits are close to some fixed point. In this paper, we study the sets of points well-approximated by...

Random Perturbations of Non-Uniformly Expanding Maps

Random perturbations of non - uniformly expanding maps ∗

We give both sufficient conditions and necessary conditions for the stochastic stability of non-uniformly expanding maps either with or without critical sets. We also show that the number of probability measures describing the statistical asymptotic behaviour of random orbits is bounded by the number of SRB measures if the noise level is small enough. As an application of these results we prove...

medium dense non-cemented carbonate sand under reversed cyclic loading

carbonate materials are mostly found in tropical areas, where exploiting gas and oil resources are of high concern. their unique behavior under shear loading first was recognised during oil resources investigations in the persian gulf. off-shore structures have been placed on carbonate soils which are highly crushable.during storms cyclic loading imposes on the bases of structures lied down on ...

Non-uniformly Expanding Dynamics in Maps with Singularities and Criticalities

We investigate a one-parameter family of interval maps arising in the study of the geometric Lorenz ow for non-classical parameter values. Our conclusion is that for all parameters in a set of positive Lebesgue measure, the map has a positive Lyapunov exponent. Furthermore, this set of parameters has a density point which plays an important dynamic role. The presence of both singular and critic...