The resonance theory for stochastic layers in nonlinear dynamic systems

Chaos, Solitons and Fractals

Volumn 12, Issue 13, 2001, Pages 2493-2508

  Luo, Albert C J ^a   Han, Ray P S ^b  

^a SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE   (United States)

^b UNIVERSITY OF IOWA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL THEORY; HAMILTONIANS; INTEGRATION; NONLINEAR CONTROL SYSTEMS; RANDOM PROCESSES;

RESONANCE THEORY; STOCHASTIC LAYERS;

CHAOS THEORY;

EID: 0035480463     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(00)00225-3     Document Type: Article

References (44)

1. A universal instability of many-dimensional oscillator systems
2. Resonant layers in nonlinear dynamics
3. Analytical predictions of chaos in a nonlinear rod
4. On the stability of the center for time periodic perturbations
5. Exponentially small splittings of separatrices with applications to KAM theory and degenerate bifurcations
6. Splitting of separatrices for standard and semistandard mappings
7. Exponentially small splitting in Hamiltonian systems
8. A refined formula for the separatrix splitting for the standard map
9. An averaging method for Hamiltonian systems, exponentially close to integrable ones
10. Width of stochastic layers in near-integrable two-dimensional symplectic maps
11. Destruction of magnetic surfaces by magnetic field irregularities: Part II
12. Stochastic instability of trapped particles and conditions of application of the quasi-linear approximation
13. Instability of dynamical systems with several degrees of freedom
14. On the behavior of trajectories of systems near to autonomous Hamiltonian systems
15. An exponential estimate of the time of stability of nearly-integrable Hamiltonian systems
16. The separation of motion in systems with rapidly rotating phase
17. Motion of a one-dimensional nonlinear oscillator under adiabatic conditions
18. Resonant-separatrix webs in stochastic layers of the twin-well Duffing oscillator
19. Motion in the vicinity of the separatrix of a nonlinear resonance in the presence of high-frequency excitations
20. Two-dimensional measure-preserving mappings
21. A method for computing the stochastic transition
22. Transport rates of a class of two-dimensional maps and flow
23. Homoclinic tangles-classification and applications
24. Secondary homoclinic bifurcation theorems
25. Scaling properties and anomalous transport of particles inside the stochastic layer
26. Self-similarity of stochastic magnetic field lines near the X-point
27. Application of the separatrix map to study perturbed magnetic field lines near the separatrix
28. Analysis of the separatrix map in Hamiltonian systems
29. Semiclassical quantization of a separatrix map
30. Field-induced barrier penetration in the quadratic potential
31. Perturbed double-well system: The pendulum approximation and low-frequency effect
32. Renormalization method for the onset of stochasticity in a Hamiltonian system
33. Stochasticity in classic Hamiltonian systems: Universal aspects
34. External field induced chaos in an infinite square well potential
35. Chaotic analysis of subharmonic resonant waves in undamped and damped strings
36. Investigations of stochastic layers in nonlinear dynamics
37. Hamiltonian algorithms for Hamiltonian systems and a comparative numerical study
38. The accuracy of symplectic integrators