Oscillator system

An oscillator system of a mechanical timepiece, comprising:

• at least one balance wheel that is free to rotate about an axis;
• and
• at least one unitary hairspring formed of a continuous, uninterrupted member and connecting the at least one balance wheel to another balance wheel, the another balance wheel having an axis offset from the axis of the at least one balance wheel, the hairspring including:
• a first coil connected to the at least one balance wheel;
• and
• a second coil connected to the another balance wheel;
• and
• a transition section connecting the first coil to the second coil;
• wherein an approximately linear restoring torque for the at least one balance wheel is primarily provided by elastic deformation of the transition section and the coils, in order to generate an oscillatory motion for the at least one balance wheel;
• and
• wherein the at least one balance wheel and the another balance wheel are identical balance wheels.