Anharmonic oscillator

Reading path

To understand this page from the ground up, read these 43 pages in order. The foundations come first.

1. Complex numbers object
2. Differential equation concept
3. Function concept
4. Hamiltonian system concept
5. Homoclinic orbit concept
6. Interval concept
7. Melnikov method concept
8. Euler's formula statement
9. Ordinary differential equation definition
10. Lipschitz condition definition
11. Grönwall's inequality statement
12. Order of a differential equation definition
13. Solution of an ordinary differential equation definition
14. Autonomous system definition
15. Initial value problem definition
16. Linear differential equation of order n definition
17. Equilibrium point definition
18. System of linear differential equations definition
19. Uniqueness of solutions for Lipschitz vector fields statement
20. Homogeneous linear equation definition
21. Linear equation with constant coefficients definition
22. Homogeneous linear system with constant coefficients definition
23. Maximal solution definition
24. Superposition principle statement
25. Characteristic equation definition
26. Matrix exponential as the solution of a linear system statement
27. Flow of a vector field definition
28. Solution space of a homogeneous linear equation has dimension n statement
29. Lyapunov stability definition
30. Trajectory definition
31. Fundamental system of solutions definition
32. Asymptotic stability definition
33. First integral definition
34. Solutions for distinct real roots statement
35. Stability of linear systems via eigenvalues statement
36. Solutions for repeated roots statement
37. Linearisation at an equilibrium concept
38. Solutions for complex conjugate roots statement
39. Hyperbolic equilibrium point definition
40. Harmonic oscillator example
41. Pendulum equation example
42. Duffing equation example
43. Anharmonic oscillator concept