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

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