Bidimensional Symplectic Maps

TL;DR

This paper introduces two symplectic maps, the standard and non-twist maps, demonstrating their effectiveness in visualizing and analyzing the dynamics of conservative systems with two degrees of freedom across various scientific fields.

Contribution

The paper presents two new examples of symplectic maps and explores their phase space transformations as control parameters change.

Findings

Effective visualization of conservative system dynamics

Phase space transformations with parameter variation

Applicability across multiple scientific disciplines

Abstract

Symplectic maps can provide a straightforward and accurate way to visualize and quantify the dynamics of conservative systems with two degrees of freedom. These maps can be easily iterated from the simplest computers to obtain trajectories with great accuracy. Their usage arises in many fields, including celeste mechanics, plasma physics, chemistry, and so on. In this paper we introduce two examples of symplectic maps, the standard and the standard non-twist map, exploring the phase space transformation as their control parameters are varied.