R S MacKay 1992 Nonlinearity 5 161 doi:10.1088/0951-7715/5/1/007
Greene's residue criterion
R S MacKay
Show affiliationsGreene (1979) proposed a relationship between the existence of an invariant circle for an area-preserving map and the 'residues' of periodic orbits with nearby rotation number. It remains without a doubt the most effective practical criterion for calculating the breakup of invariant circles. In this work four results are proved which go a long way towards placing the criterion on a rigorous foundation, and the issues remaining to be resolved in order to formulate a rigorous version of the criterion are discussed.
- PACS
- MSC
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37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
37J40 Perturbations, normal forms, small divisors, KAM theory, Arnol'd diffusion
70K43 Quasi-periodic motions and invariant tori
37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction (See also 53D20)
- Subjects
- Dates
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Issue 1 (January 1992)
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Greene's residue criterion
R S MacKay 1992 Nonlinearity 5 161
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Quality-of-service specification in distributed object systems
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Observation of strong exciton–photon coupling at temperatures up to 410 K
Chris Sturm et al 2009 New J. Phys. 11 073044
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