A system for closing a glass door which is supported by a floor, the door being movable between an open position and a closed position, the system comprising: - a door closing hinge; - a mounting plate to be anchored on the floor by suitable fasteners; wherein the door closing hinge comprises: - a fix element anchorable to the floor through the mounting plate; - a movable element anchorable to the door, the movable element being rotatably coupled to the fix one to rotate about a first longitudinal axis between the open door position and the closed door position; - said movable element comprising a box-shaped body, said fix element comprising a pin which defines the first longitudinal axis; - closing means for the automatic return of the door from the open to the closed position, said closing means comprising a first cam element interacting with a first plunger element movable within said box-shaped body between a first compressed end position corresponding to the open door position and a first extended end position corresponding to the closed door position; - braking means acting on said closing means for counteracting the action thereof, said braking means comprising a second cam element interacting with a second plunger element movable within said box-shaped body between a second compressed end position, corresponding to the closed door position and a second extended end position, corresponding to the open door position; wherein - both said first and second cam elements ( 31, 41) are unitary with said pin; - said pin is interposed between said first and second plunger elements ( 32, 42), the latter ( 32, 42) being reciprocally opposite with respect to said pin; - said first and second plunger elements ( 32, 42) are both slidably movable along a second axis substantially perpendicular to said first axis, the box-shaped body having an elongated shape along said second axis; wherein said first plunger element comprises a substantially cylindrical first back portion and a first front portion ( 32 ") including at least one first pushing head ( 33, 33 '), said second plunger element comprising a substantially cylindrical second back portion ( 42 ') and a second front portion ( 42 ") which include at least one second pushing head, characterized in that said first and second plunger elements (32, 42) are slidably movable in a single operating chamber defining said second axis through which said first and second plunger elements (32, 42) are coaxially inserted, in that said operating chamber comprises a working fluid, said first and second back portions ( 32', 42 ') being designed to separate said operating chamber into a first, a second and a third adjacent variable volume compartments ( 51, 52, 53) in reciprocal fluidic communication, and further characterized in that said operating chamber comprises control means for controlling the flow of the working fluid designed to allow the flow thereof from said first compartment to said third compartment through said second compartment upon the opening of the door and to allow the backflow thereof from said third compartment to said first compartment through said second compartment upon the closing of the door. - a door closing hinge; - a mounting plate to be anchored on the floor by suitable fasteners; - a fix element anchorable to the floor through the mounting plate; - a movable element anchorable to the door, the movable element being rotatably coupled to the fix one to rotate about a first longitudinal axis between the open door position and the closed door position; - said movable element comprising a box-shaped body, said fix element comprising a pin which defines the first longitudinal axis; - closing means for the automatic return of the door from the open to the closed position, said closing means comprising a first cam element interacting with a first plunger element movable within said box-shaped body between a first compressed end position corresponding to the open door position and a first extended end position corresponding to the closed door position; - braking means acting on said closing means for counteracting the action thereof, said braking means comprising a second cam element interacting with a second plunger element movable within said box-shaped body between a second compressed end position, corresponding to the closed door position and a second extended end position, corresponding to the open door position; wherein - both said first and second cam elements ( 31, 41) are unitary with said pin; - said pin is interposed between said first and second plunger elements ( 32, 42), the latter ( 32, 42) being reciprocally opposite with respect to said pin; - said first and second plunger elements ( 32, 42) are both slidably movable along a second axis substantially perpendicular to said first axis, the box-shaped body having an elongated shape along said second axis;