COCYCLES WITH QUASI-CONFORMALITY I: STABILITY AND ABUNDANCE

2024/08/25 by Meysam Nassiri, Hesam Rajabzadeh, Nassiri, Meysam +3 · 1 citation
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Chaos control and synchronization #Mathematical Dynamics and Fractals

paper · pdf · doi:10.1017/s1474748025101369

Abstract

Abstract 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 \mathcal C^α -stably exhibit fiberwise bounded orbits ( α>0 ). The proof is based on a new mechanism which yields stable elliptic-type behavior in \mathrm GL(d,\mathbb R) or \mathrm SL(d,\mathbb R) cocycles. Moreover, we show that this phenomenon is \mathcal C⁰ -dense among \mathrm SL(d,\mathbb R) cocycles over a shift of finite type without dominated splitting.

Citations

• Extremal Lyapunov exponents: an invariance principle and applications
• Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents

Cited by

• Removing quasiconformal orbits

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