# Multiple periodic solutions for one-sided sublinear systems: A refinement of the Poincar\'{e}-Birkhoff approach

## TL;DR

This paper establishes the existence of multiple harmonic and subharmonic solutions for certain planar Hamiltonian systems with sublinear nonlinearities, using refined Poincaré-Birkhoff methods and complex dynamics analysis.

## Contribution

It introduces refinements to the Poincaré-Birkhoff approach and extends the analysis to complex dynamics for sublinear Hamiltonian systems.

## Key findings

- Multiple periodic solutions are proven to exist.
- Refined methods improve solution multiplicity results.
- Complex dynamics are analyzed within the system.

## Abstract

In this paper we prove the existence of multiple periodic solutions (harmonic and subharmonic) for a class of planar Hamiltonian systems which include the case of the second order scalar ODE $x'' + a(t)g(x) = 0$ with $g$ satisfying a one-sided condition of sublinear type. We consider the classical approach based on the Poincar\'{e}-Birkhoff fixed point theorem as well as some refinements on the side of the theory of bend-twist maps and topological horseshoes. The case of complex dynamics is investigated, too.