Abstract
An expression for the quasi-random jump of the adiabatic invariant at a separatrix crossing is obtained for a slow–fast Hamiltonian system with two degrees of freedom in the case when the separatrix passes through a degenerate saddle point in the phase plane of the fast variables. The general case with an arbitrary degree of degeneracy was considered, and this degree is assumed to remain fixed in the process of evolution of the slow variables. The typical value of the jump is larger than in the non-degenerate case studied earlier. Though strongly degenerate, such a setting can be relevant for physical problems. The influence of the asymmetry of a phase portrait on the magnitude of adiabatic invariant jumps was considered as well. An example of this kind is studied, namely the motion of ions in current sheets with complex inner structure.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
