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 (TC ) 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.

In this paper we study the dynamics of the standard map, in the conservative, dissipative and dissipative relativistic regimes, through a numerical approach. For the three cases above, were built their phase spaces, for through them, we can observe the existence and organization of periodic and chaotic domains. We also investigate the influence of the term in the relativistic dynamics of relativistic dissipative standard map and perform an analysis of how dissipation changes the structure of the phase space and quasi-periodic orbits.