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We study the breakdown of rotational invariant tori in 2D and 4D standardmaps by implementing three different methods. First, we analyze the domains ofanalyticity of a torus with given frequency through the computation of theLindstedt series expansions of the embedding of the torus and the drift term.The Pad\'e approximants provide the shape of the analyticity domains byplotting the poles of the polynomial at the denominator of the approximants.Secondly, we implement a Newton method to construct the embedding of the torus;the breakdown threshold is then estimated by looking at the blow-up of theSobolev norms of the embedding. Finally, we implement an extension of Greenemethod to get information on the breakdown threshold of an invariant torus withirrational frequency by looking at the stability of the periodic orbits withperiods approximating the frequency of the torus.  We apply these methods to 2D and 4D standard maps. The 2D maps can either beconservative (symplectic) or dissipative ( more precisely, conformallysymplectic, namely a dissipative map with the geometric property to transformthe symplectic form into a multiple of itself). The 4D maps are obtainedcoupling $(i)$ two symplectic standard maps, or $(ii)$ two conformallysymplectic standard maps, or $(iii)$ a symplectic and a conformally symplecticstandard map.  Concerning the results, Pad\'e and Newton methods perform well and providereliable and consistent results (although we implemented Newton method only forsymplectic and conformally symplectic maps). Our implementation of theextension of Greene method is inconclusive, since it is computationallyexpensive and delicate, especially in 4D non-symplectic maps, also due to theexistence of Arnold tongues.

Breakdown of rotational tori in 2D and 4D conservative and dissipative standard maps