arXiv subjects

Bharath Krishna Seshadri

Publications and source records attributed to Bharath Krishna Seshadri.

4 recordsLinked to original sources

arXiv2026

Uniqueness of the equilibrium state in the dynamics of holomorphic correspondences

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 Riemann sphere. We mainly work with the correspondence restricted on the support of the Dinh-Sibony measure and identify topologically interesting correspondences, namely distance expanding ones. Further, we consider Hölder continuous potentials defined on the support of the Dinh-Sibony measure, for which we prove the uniqueness of equilibrium state. Along the way, we also prove some interesting topological results related to holomorphic correspondences. Finally, we establish a result connecting the Ruelle operator for holomorphic correspondences and the unique equilibrium state under a suitable hypothesis. The concluding part of the paper is devoted to some discussion related to the hypothesis involved and providing some examples.

math.DS↗

arXiv2026

A classification of restrictive polynomial correspondences

In this manuscript, we study a special class of correspondences on $\mathbb{P}^{1} \times \mathbb{P}^{1}$ given by a polynomial relation, say $P(z, w)$. We focus on what we call restrictive polynomial correspondence and characterise that it can be written as $P (z, w) = g_{1}(w) h_{1}(z) + \cdots + g_ρ(w) h_ρ(z)$, for some appropriate $ρ\in \mathbb{Z}_{+}$, where $g_{r}$ and $h_{r}$ are polynomials. In particular, when $ρ= 2$, we say $P$ is irreducible and observe that the equation $P(z, w) = 0$ can be rewritten as $R(z) = S(w)$, where $R$ and $S$ are rational maps of appropriate degree. Further, we also define an operation that, with the exception of degenerate cases, constructs a new irreducible restrictive polynomial correspondence from any two given irreducible restrictive polynomial correspondences.

math.GM↗

arXiv2026

A view towards mixing in holomorphic correspondences

In this manuscript we develop a theory of mixing and weakly mixing in the study of dynamics of holomorphic correspondences defined on a compact connected complex manifold. We also connect these notions to the theory of ergodicity of holomorphic correspondences developed by Londhe. Further, we give motivation and illustrative examples that compare the present scenario with that of maps. Finally, we study product of two holomorphic correspondences and use them to characterise weakly mixing.

math.DS↗

arXiv2025

Counting functions over periodic orbits of a skew-product map

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 to a finitely generated rational semigroup. To be precise, we obtain some comparability results for the above mentioned counting functions.

math.DS↗