Stronger Lasota-Yorke inequality for one-dimensional piecewise expanding transformations
نویسندگان
چکیده
منابع مشابه
Stronger Lasota-yorke Inequality for One-dimensional Piecewise Expanding Transformations
For a large class of piecewise expanding C1,1 maps of the interval we prove the Lasota-Yorke inequality with a constant smaller than the previously known 2/ inf |τ ′|. Consequently, the stability results of Keller-Liverani [7] apply to this class and in particular to maps with periodic turning points. One of the applications is the stability of acim’s for a class of W-shaped maps. Another appli...
متن کاملUlam's Method for Lasota-Yorke Maps with Holes
Ulam’s method is a rigorous numerical scheme for approximating invariant densities of dynamical systems. The phase space is partitioned into connected sets and an inter-set transition matrix is computed from the dynamics; an approximate invariant density is read off as the leading left eigenvector of this matrix. When a hole in phase space is introduced, one instead searches for conditional inv...
متن کاملON THE EXISTENCE OF INVARIANT MEASURES FOR PIECEWISE MONOTONIC TRANSFORMATIONS ( l ) BY A . LASOTA AND
A class of piecewise continuous, piecewise C transformations on the interval [O, l] is shown to have absolutely continuous invariant measures.
متن کاملStability and Approximation of Random Invariant Densities for Lasota-yorke Map Cocycles
We establish stability of random absolutely continuous invariant measures (acims) for cocycles of random Lasota-Yorke maps under a variety of perturbations. Our family of random maps need not be close to a fixed map; thus, our results can handle very general driving mechanisms. We consider (i) perturbations via convolutions, (ii) perturbations arising from finite-rank transfer operator approxim...
متن کاملA Spectral Gap for a One-dimensional Lattice of Coupled Piecewise Expanding Interval Maps
We study one-dimensional lattices of weakly coupled piecewise expanding interval maps as dynamical systems. Since neither the local maps need to have full branches nor the coupling map needs to be a homeomorphism of the infinite dimensional state space, we cannot use symbolic dynamics or other techniques from statistical mechanics. Instead we prove that the transfer operator of the infinite dim...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2013
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2013-11676-x