Wavelet approach to accelerator problems. 3: Melnikov functions and symplectic topology

Conference · Thu May 01 04:00:00 EDT 1997

OSTI ID:521654

Fedorova, A; Zeitlin, M ^[1]; Parsa, Z ^[2]

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1. Russian Academy of Sciences, St. Petersburg (Russian Federation). Inst. of Problems of Mechanical Engineering
2. Brookhaven National Lab., Upton, NY (United States). Dept. of Physics

This is the third part of a series of talks in which the authors present applications of methods of wavelet analysis to polynomial approximations for a number of accelerator physics problems. They consider the generalization of the variational wavelet approach to nonlinear polynomial problems to the case of Hamiltonian systems for which they need to preserve underlying symplectic or Poissonian or quasicomplex structures in any type of calculations. They use the approach for the problem of explicit calculations of Arnold-Weinstein curves via Floer variational approach from symplectic topology. The loop solutions are parameterized by the solutions of reduced algebraical problem--matrix Quadratic Mirror Filters equations. Also they consider wavelet approach to the calculations of Melnikov functions in the theory of homoclinic chaos in perturbed Hamiltonian systems.

• Research Organization: Brookhaven National Lab., Upton, NY (United States)
• Sponsoring Organization: USDOE Office of Energy Research, Washington, DC (United States)
• DOE Contract Number: AC02-76CH00016
• OSTI ID: 521654
• Report Number(s): BNL--64501; CAP--172-MISC-97C; CONF-970503--200; ON: DE97007724
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
99 GENERAL AND MISCELLANEOUS
ACCELERATORS
BEAM DYNAMICS
FUNCTIONS
NONLINEAR PROBLEMS
TOPOLOGY
VARIATIONAL METHODS