A system for cutting grass comprising: a lawn mower provided with: - movement means for moving said lawn mower in a cutting area; - one or more blades for cutting grass in said cutting area; a perimeter cable, delimiting said cutting area, in which a perimeter electrical signal is propagated; at least one means (MSi; i= 1...n) for signalling a path change (ΔPi; i= 1...n) associated with said perimeter cable, - wherein said means (MSi; i=1...n) for signalling a path change (ΔPi; i= 1...n) is configured to signal to said lawn mower a path change (ΔPi) relative to a predefined path (PPRED) provided for by the predefined operation of said lawn mower; - wherein said path change (ΔPi) is signalled to said lawn mower by means of an encoded signal (Si; i=1...n) generated by said signalling means (MSi; i= 1...n); - wherein said signalling means (MSi; i= 1...n) is powered by an electromotive force (fem) induced by a magnetic field generated on the basis of said perimeter electrical signal; wherein said lawn mower further comprises: - a sensor means configured to sense said encoded signal (Si); - a processing unit associated with said sensor means and configured to actuate said movement means as a function of said sensed encoded signal (Si) so that said movement means are moved in order to cause the lawn mower to make said path change (ΔPi); wherein said at least one signalling means (MSi; i1...n) defines for said lawn mower, via said path change (ΔPi), at least one portion of an optimal path (POPT) for reaching a target point relative to said predefined path (PPRED) provided for by the predefined operation of said lawn mower; characterised in that said means (MSi; i=1...n) for signalling a path change (ΔPi; i=1...n) is configured to be movable within said cutting area in order to define a new optimal path (POPT) as a function of a modification of said target point. a lawn mower provided with: - movement means for moving said lawn mower in a cutting area; - one or more blades for cutting grass in said cutting area; - movement means for moving said lawn mower in a cutting area; - one or more blades for cutting grass in said cutting area; a perimeter cable, delimiting said cutting area, in which a perimeter electrical signal is propagated; at least one means (MSi; i= 1...n) for signalling a path change (ΔPi; i= 1...n) associated with said perimeter cable, - wherein said means (MSi; i=1...n) for signalling a path change (ΔPi; i= 1...n) is configured to signal to said lawn mower a path change (ΔPi) relative to a predefined path (PPRED) provided for by the predefined operation of said lawn mower; - wherein said path change (ΔPi) is signalled to said lawn mower by means of an encoded signal (Si; i=1...n) generated by said signalling means (MSi; i= 1...n); - wherein said signalling means (MSi; i= 1...n) is powered by an electromotive force (fem) induced by a magnetic field generated on the basis of said perimeter electrical signal; - wherein said means (MSi; i=1...n) for signalling a path change (ΔPi; i= 1...n) is configured to signal to said lawn mower a path change (ΔPi) relative to a predefined path (PPRED) provided for by the predefined operation of said lawn mower; - wherein said path change (ΔPi) is signalled to said lawn mower by means of an encoded signal (Si; i=1...n) generated by said signalling means (MSi; i= 1...n); - wherein said signalling means (MSi; i= 1...n) is powered by an electromotive force (fem) induced by a magnetic field generated on the basis of said perimeter electrical signal; wherein said lawn mower further comprises: - a sensor means configured to sense said encoded signal (Si); - a processing unit associated with said sensor means and configured to actuate said movement means as a function of said sensed encoded signal (Si) so that said movement means are moved in order to cause the lawn mower to make said path change (ΔPi); - a sensor means configured to sense said encoded signal (Si); - a processing unit associated with said sensor means and configured to actuate said movement means as a function of said sensed encoded signal (Si) so that said movement means are moved in order to cause the lawn mower to make said path change (ΔPi); wherein said at least one signalling means (MSi; i1...n) defines for said lawn mower, via said path change (ΔPi), at least one portion of an optimal path (POPT) for reaching a target point relative to said predefined path (PPRED) provided for by the predefined operation of said lawn mower;