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…
Twisted cocycle for interval exchange transformations: Invariant structures and Lyapunov spectrum
Hesam Rajabzadeh, Pedram Safaee
This paper investigates the algebraic and dynamical properties of the twisted cocycle, a -valued cocycle defined over the toral extension of the Zorich…
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 $\…
Nondegeneracy of the spectrum of the twisted cocycle for interval exchange transformations
Hesam Rajabzadeh, Pedram Safaee
We prove the positivity of the top Lyapunov exponent of the twisted (spectral) cocycle, associated with IETs, with respect to a family of natural invariant measures. The proof reli…
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…