5 papers
Cocycles with Quasi-Conformality II: Ergodic measures with positive entropy
Meysam Nassiri, Hesam Rajabzadeh, Zahra Reshadat
As the second part of a series on linear cocycles over chaotic systems, this paper establishes a "multiple covering principle" that robustly yields positive-entropy ergodic measure…
Cantor sets in higher dimensions II: Optimal dimension constraint for stable intersections
Meysam Nassiri, Mojtaba Zareh Bidaki
It is well known that a pair of compact sets in () can be separated by small deformations if the sum of their upper box dimensions is less than …
Cantor sets in higher dimension I: Criterion for stable intersections
Meysam Nassiri, Mojtaba Zareh Bidaki
We study the geometry of dynamically defined Cantor sets in arbitrary dimensions, introducing a criterion for stable intersections of such Cantor sets, under a…
Cocycles with Quasi-Conformality I: Stability and abundance
Meysam Nassiri, Hesam Rajabzadeh, Zahra Reshadat
This is the first part of a series of papers devoted to the study of linear cocycles over chaotic systems. In the present paper, we establish the existence of such cocycles that $\…
Stable local dynamics: expansion, quasi-conformality and ergodicity
Abbas Fakhari, Meysam Nassiri, Hesam Rajabzadeh
In this paper, we study stable ergodicity of the action of groups of diffeomorphisms on smooth manifolds. Such actions are known to exist only on one-dimensional manifolds. The aim…