My research is related to low dimensional dynamics, including  circle maps and holomorphic dynamics in dimension one. One of the things that I have studied is a class of circle maps that can be considered as Perturbations of the Doubling Map. This was inspired by the 2007 work of Misiurewicz and Rodrigues where they introduced and studied a specific family of maps which are  in fact Perturbations of the Doubling Map . They gave this family a very interesting name- Double Standard Family. 

     I have also studied topological dynamical systems in dimension one and two. My goal was to find connections between the exponential growth rate of length of a typical curve under iteration  and topological entropy, turbulence and other chaotic properties of such systems . This theme goes back to the 1980 paper by Misiurewicz and Szelnk .  I am also interested in ergodic theory, in particular,  smooth ergodic theory, thermodynamic formalism and ergodic structure theory.  

Here is a list of publications and preprints related to to my research. 

[1]  K. Banerjee, A. Bhattacharyya, S. Mondal, Total Variation of a curve under Chaos on the Real line and on a finite graph, Qualitative Theory of Dynamical Systems 23 (1), 16,  2024. 

[2]  K. Banerjee, A. Bhattacharyya, Paths of analytic circle diffeomorphisms,  book chapter in Contemporary mathematics, Proceedings of the 29th ICFIDCAA(2023),  American Mathematical Society, 2025.

[3]  K. Banerjee, A. Bhattacharyya, S. Mondal, Total variation and Chaos on the unit square, Journal of Difference Equations and Applications 31 (11), 1418-1430, 2025.  

[4]  K. Banerjee, A. Bhattacharyya, S. Mukherjee, Uniformization of tongues in Double Standard Map family and variation of maximal chaotic sets, https://arxiv.org/abs/2505.02189 , Submitted.

[5]  A. Bhattacharyya, K. Banerjee, On the Piecewise Linear Perturbations of the Doubling Map, http://arxiv.org/abs/2510.11441 .

[6]  K. Banerjee, A. Bhattacharyya, S. Mondal, Topological entropy, chaos and total variation of a curve, accepted for publication as a book chapter in upcoming Contemporary mathematics — Proceedings of the AMS Special Session on Topics in Complex Analysis and Dynamics in Honor of Professor Yunping Jiang on the Occasion of his 65th Birthday.