Adiabatic invariants for dynamical systems with one degree of freedom

Adiabatic invariants for dynamical systems with one degree of freedom, whose equation of motion is (1), and where the existence of the corresponding Hamilton action integral is not imposed, are established. The adiabatic invariants may vary according to their structure. Using the theory a few particular problems, including non-autonomous Duffing and Van der Pol oscillators, are analysed. Finally, it is indicated how the adiabatic invariants can be used for finding approximate solutions, stability analyses and for plotting phase curves.