Shrihari Sridharan

On induced systems and ergodicity for holomorphic correspondences

Sathi Trikkadeeri Mana, Shrihari Sridharan

The Poincaré recurrence theorem for a holomorphic correspondence provides a natural framework for studying the first return time and a dynamical system thus induced, in this settin…

Uniqueness of the equilibrium state in the dynamics of holomorphic correspondences

Bharath Krishna Seshadri, Shrihari Sridharan

This paper concerns the study of the existence of a unique equilibrium state for a Hölder continuous function under the dynamics of a holomorphic correspondence defined on the Riem…

A multiplicative ergodic theorem in random and simultaneous dynamics

Thirupathi Perumal, Shrihari Sridharan

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 dyn…

A variational principle for holomorphic correspondences

Subith Gopinathan, Shrihari Sridharan

In this paper, we consider a dynamical system on the Riemann sphere that evolves through a set-valued map, namely a holomorphic correspondence. Analogous to the investigation of th…

math.DS2025

Extremal Lyapunov exponents in random and simultaneous dynamics

Thirupathi Perumal, Shrihari Sridharan

In this manuscript, we consider finitely many maps, all of which are defined on a compact probability space, with at least one map in the collection having degree strictly bigger t…

math.DS2025

Counting functions over periodic orbits of a skew-product map

Subith Gopinathan, Bharath Krishna Seshadri, Shrihari Sridharan

In this manuscript, we investigate some properties of certain counting functions, associated to the ergodic sums computed along the periodic orbits of the skew-product map, related…

math.DS2024

A Ruelle operator for holomorphic correspondences

Shrihari Sridharan, Subith G

In this paper, we extend the ideas of certain notions that one studies in thermodynamic formalism of maps to the context when the dynamics in the phase space evolves by complex hol…

math.DS2023

Polynomial correspondences expressible as maps of $d$ -tuples

Shrihari Sridharan, Subith G., Atma Ram Tiwari

In this paper, we consider polynomial correspondences $f (x, y)$ in $C [x, y]$ of degree $d \geq 2$ in both the variables and obtain necessary and sufficient conditions in o…

math.DS2021

Dynamics of Products of Matrices in Max Algebra

S. Jayaraman, Y. K. Prajapaty, S. Sridharan

The aim of this manuscript is to understand the dynamics of matrix products in a max algebra. A consequence of the Perron-Fröbenius theorem on periodic points of a nonnegative matr…

Dynamics of products of nonnegative matrices

Sachindranath Jayaraman, Yogesh Kumar Prajapaty, Shrihari Sridharan

The aim of this manuscript is to understand the dynamics of products of nonnegative matrices. We extend a well known consequence of the Perron-Frobenius theorem on the periodic poi…

Weak Formulation of the Laplacian on the Full Shift Space

Shrihari Sridharan, Sharvari Neetin Tikekar

We consider a Laplacian on the one-sided full shift space over a finite symbol set, which is constructed as a renormalized limit of finite difference operators. We propose a weak d…

Simultaneous Action of Finitely Many Interval Maps: Some Dynamical and Statistical Properties

Aswin Gopakumar, Kirthana Rajasekar, Shrihari Sridharan

In this paper, we consider finitely many interval maps simultaneously acting on the unit interval $I = [0, 1]$ in the real line $R$ ; each with utmost finitely many jump di…

The entropy of holomorphic correspondences: exact computations and rational semigroups

Gautam Bharali, Shrihari Sridharan

We study two notions of topological entropy of correspondences introduced by Friedland and Dinh-Sibony. Upper bounds are known for both. We identify a class of holomorphic correspo…

Dirichlet eigenvalues of the Laplacian on full one-sided shift space

Shrihari Sridharan, Sharvari Neetin Tikekar

The full one sided shift space over finite symbols is approximated by an increasing sequence of finite subsets of the space. The Laplacian on the space is then defined as a renorma…

Lyapunov exponents of polynomials with respect to certain weighted Lyubich's measures

Shrihari Sridharan, Atma Ram Tiwari

In this paper, we consider a monic, centred, hyperbolic polynomial of degree $d \geq 2$ , restricted on its Julia set and compute its Lyapunov exponents with respect to certain weigh…

math.DS2019★ 1 cited

A Laplacian on the Full Shift Space

Shrihari Sridharan, Sharvari Neetin Tikekar

In this paper, we consider the one-sided shift space on finitely many symbols and extend the theory of what is known as rough analysis. We define difference operators on an increas…

Distribution of typical orbits for a skew-product map generated by random dynamics of finitely many rational maps

Shrihari Sridharan, Sharvari Neetin Tikekar, Atma Ram Tiwari

In this paper, we consider the dynamics of a skew-product map defined on the Cartesian product of the symbolic one-sided shift space on $N$ symbols and the complex sphere where we…