• Pendulum
• Double well
• Lennard-Jones
• Circular Landau oscillator

Lennard-Jones

$$U(x)=\frac{1}{x^{12}}-\frac{1}{x^6}$$ The graphs below show the potential, and the phase space of a particle submitted to the Lennard-Jones potential

• for $E\in (-1/4,0)$: oscillations
• for $E\in (0,\mathrm{\infty })$: asymptotically free
• for $E=0$: separatrix: the interaction has an infinite range.

Energy: - + E=0.1

Stop!