# The effect of temperature on generic stable periodic structures in the parameter space of dissipative relativistic standard map

## TL;DR

This paper investigates how thermal noise influences the stability of periodic structures in a dissipative relativistic standard map, showing that increased temperature can suppress stable periodic behaviors without fully stochasticizing the system.

## Contribution

It introduces a detailed analysis of thermal effects on stable periodic structures in a relativistic map, using Lyapunov exponents to determine critical temperatures for structure destruction.

## Key findings

- Thermal noise suppresses stable periodic structures in the parameter space.
- Smaller structures are affected first, starting from their borders.
- Critical temperatures are identified where chaos dominates.

## Abstract

In this work, we have characterized changes in the dynamics of a two-dimensional relativistic standard map in the presence of dissipation and specially when it is submitted to thermal effects modeled by a Gaussian noise reservoir. By the addition of thermal noise in the dissipative relativistic standard map (DRSM) it is possible to suppress typical stable periodic structures (SPSs) embedded in the chaotic domains of parameter space for large enough temperature strengths. Smaller SPSs are first affected by thermal effects, starting from their borders, as a function of temperature. To estimate the necessary temperature strength capable to destroy those SPSs we use the largest Lyapunov exponent to obtain the critical temperature ($T_C$) diagrams. For critical temperatures the chaotic behavior takes place with the suppression of periodic motion, although, the temperature strengths considered in this work are not so large to convert the deterministic features of the underlying system into a stochastic ones.