arXiv subjects

Thirupathi Perumal

Publications and source records attributed to Thirupathi Perumal.

2 recordsLinked to original sources

arXiv2026

A multiplicative ergodic theorem in random and simultaneous dynamics

In this manuscript, we consider finitely many maps defined on a compact probability space; each of which preserves the probability measure. We consider two aspects of growth of dynamical systems in this scenario; the first setting where we let some infinite lettered word determine the path through which the orbit of points evolve, while the second setting where we consider all possible paths through which the orbit of a set may evolve. Our aim in this paper is to provide a full description of the celebrated multiplicative ergodic theorem, originally due to Oseledets, for such dynamical systems that is point-valued (as in the first case) and set-valued (as in the second case).

math.DS↗

arXiv2025

Extremal Lyapunov exponents in random dynamics

In this manuscript, we consider finitely many maps, all of which are defined on a smooth compact measure space, with at least one map in the collection having degree strictly bigger than 1. Working with random dynamics generated by this setting, we obtain an expression for the extremal Lyapunov exponents, that characterise the instability of typical orbits, as the limit of the averages of the logarithm of the operator norm of linear cocycles of generic orbits. We obtain this as a consequence to the Kingman's ergodic theorem for a subadditive sequence of measurable functions, which naturally generalises the Birkhoff's ergodic theorem.

math.DS↗