Double-acting pressure reducing cylinder with adaptive support comprising a cylinder shaft, cooperating with a double-acting pressure reducing piston which is connected by a lower piston rod to means of transmission installed in a transmission casing to which the cylinder shaft is secured, while the end of said shaft which emerges from the side of said means is closed by a lower cylinder head through which the lower piston rod passes via a lower rod opening to define with the double-acting pressure reducing piston a lower chamber of hot gases, while the other end of said shaft is closed by an upper cylinder head to define with said piston an upper chamber of hot gases, characterized in that it comprises: • At least one hollow pillar through which passes entirely in the direction of its length a rod tunnel, a first pillar end of said pillar resting directly or indirectly on the transmission casing, while a second pillar end of said pillar directly or indirectly supports the cylinder shaft, the lower cylinder head and the upper cylinder head, while said first end can pivot about a ball joint and/or bend in relation to said casing, while said second end can pivot about a ball joint and/or bend in relation to said cylinder shaft; • At least one tie rod, installed in the rod tunnel, a first rod end of said tie rod being directly or indirectly secured to the transmission casing, while a second rod end of said tie rod is secured to the cylinder shaft and/or to the lower cylinder head and/or to the upper cylinder head, said first end being able to pivot about a ball joint and/or bend in relation to said casing, while said second end can pivot about a ball joint and/or bend in relation to said cylinder; • Lower cylinder centering means positioned near the lower cylinder head, said means bearing against the cylinder shaft or the lower cylinder head, on the one hand, and directly or indirectly against the transmission casing on the other hand, and said means leaving the cylinder shaft free to move in parallel with its longitudinal axis in relation to the transmission casing, yet preventing said shaft from moving in the plane perpendicular to said axis, again with respect to said casing; • Upper cylinder centering means positioned near the upper cylinder head, said means bearing against the cylinder shaft or the upper cylinder head, on the one hand, and against a centering frame rigidly fixed to the transmission casing and maintained at a height near that of the upper cylinder head by at least one rigid frame pillar, on the other hand, said means leaving the cylinder shaft free to move in parallel with its longitudinal axis in relation to the transmission casing, yet preventing said shaft from moving in the plane perpendicular to said axis, again with respect to said casing. • At least one hollow pillar through which passes entirely in the direction of its length a rod tunnel, a first pillar end of said pillar resting directly or indirectly on the transmission casing, while a second pillar end of said pillar directly or indirectly supports the cylinder shaft, the lower cylinder head and the upper cylinder head, while said first end can pivot about a ball joint and/or bend in relation to said casing, while said second end can pivot about a ball joint and/or bend in relation to said cylinder shaft; • At least one tie rod, installed in the rod tunnel, a first rod end of said tie rod being directly or indirectly secured to the transmission casing, while a second rod end of said tie rod is secured to the cylinder shaft and/or to the lower cylinder head and/or to the upper cylinder head, said first end being able to pivot about a ball joint and/or bend in relation to said casing, while said second end can pivot about a ball joint and/or bend in relation to said cylinder; • Lower cylinder centering means positioned near the lower cylinder head, said means bearing against the cylinder shaft or the lower cylinder head, on the one hand, and directly or indirectly against the transmission casing on the other hand, and said means leaving the cylinder shaft free to move in parallel with its longitudinal axis in relation to the transmission casing, yet preventing said shaft from moving in the plane perpendicular to said axis, again with respect to said casing; • Upper cylinder centering means positioned near the upper cylinder head, said means bearing against the cylinder shaft or the upper cylinder head, on the one hand, and against a centering frame rigidly fixed to the transmission casing and maintained at a height near that of the upper cylinder head by at least one rigid frame pillar, on the other hand, said means leaving the cylinder shaft free to move in parallel with its longitudinal axis in relation to the transmission casing, yet preventing said shaft from moving in the plane perpendicular to said axis, again with respect to said casing.