# Superintegrable deformations of oscillator and Coulomb systems

## TL;DR

This paper explores advanced mathematical models of oscillator and Coulomb systems using complex coordinates, introducing new superintegrable systems and their supersymmetric extensions to deepen understanding of their symmetries and properties.

## Contribution

It introduces complex Euclidean and projective analogues of classical systems, expanding the class of superintegrable models with supersymmetric extensions.

## Key findings

- Complex Euclidean analogue of Smorodinsky-Winternitz system introduced
- Complex projective analogue of Rosochatius model discussed
- Supersymmetric extensions of these models considered

## Abstract

Generalizations of oscillator and Coulomb models are discussed via introduction of holomorphic coordinates. Complex Euclidean analogue of the Smorodinsky-Winternitz system is introduced and studied. Complex projective analogue of Rosochatius model is also discussed. Supersymmetric extensions of these models are considered.