arXiv subjects
Publications and source records attributed to Mikko Stenlund.
We define a quantitative notion of shear for limit cycles of flows. We prove that strange attractors and SRB measures emerge when systems exhibiting limit cycles with sufficient shear are subjected to periodic pulsatile drives. The strange attractors possess a number of precisely-defined dynamical properties that together imply chaos that is both sustained in time and physically observable.
For Dynamical Systems, a strong bound on multiple correlations implies the Central Limit Theorem (CLT) [ChMa]. In Chernov's paper [Ch2], such a bound is derived for dynamically Holder continuous observables of dispersing Billiards. Here we weaken the regularity assumption and subsequently show that the bound on multiple correlations follows directly from the bound on pair correlations. Thus, a strong bound on pair correlations alone implies the CLT, for a wider class of observables. The result is extended to Anosov diffeomorphisms in any dimension.
This paper concerns the propagation of particles through a quenched random medium. In the one- and two-dimensional models considered, the local dynamics is given by expanding circle maps and hyperbolic toral automorphisms, respectively. The particle motion in both models is chaotic and found to fluctuate about a linear drift. In the proper scaling limit, the cumulative distribution function of the fluctuations converges to a Gaussian one with system dependent variance while the density function shows no convergence to any function. We have verified our analytical results using extreme precision numerical computations.
We establish a quenched Central Limit Theorem (CLT) for a smooth observable of random sequences of iterated linear hyperbolic maps on the torus. To this end we also obtain an annealed CLT for the same system. We show that, almost surely, the variance of the quenched system is the same as for the annealed system. Our technique is the study of the transfer operator on an anisotropic Banach space specifically tailored to use the cone condition satisfied by the maps.
We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, devising an asymptotic expansion for the splitting (matrix) associated with a homoclinic point. This expansion consists of contributions that are manifestly exponentially small in the limit of vanishing hyperbolicity, by a shift-of-contour argument. Hence, we infer a similar upper bound on the splitting itself.
We consider pairs of toral automorphisms (A,B) satisfying an invariant cone property. At each iteration, A acts with probability p and B with probability 1-p. We prove exponential decay of correlations for a class of Holder continuous observables.
We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, giving a simple construction of unstable KAM tori and their stable and unstable manifolds for analytic perturbations. We extend analytically the solutions of the equations of motion, order by order in the perturbation parameter, to a uniform neighbourhood of the time axis.