Backlund transformations and divisor doubling

Abstract

In classical mechanics well-known cryptographic algorithms and protocols can be very useful for construction canonical transformations preserving form of Hamiltonians. We consider application of a standard generic divisor doubling for construction of new auto Bäcklund transformations for the Lagrange top and Hénon-Heiles system separable in parabolic coordinates.

13 pages, LaTeX with AMS fonts, 2 figures

References in corpus (4)

• Simultaneous separation for the Neumann and Chaplygin systems
• New bi-Hamiltonian systems on the plane
• Bäcklund transformations for the nonholonomic Veselova system
• Integrable discretization and deformation of the nonholonomic Chaplygin ball

Cited by in corpus (7)

• Bäcklund transformations for the nonholonomic Veselova system
• Integrable discretization and deformation of the nonholonomic Chaplygin ball
• The Kepler problem: polynomial algebra of non-polynomial first integrals
• Discretization and superintegrability all rolled into one
• On exact discretization of the cubic-quintic Duffing oscillator
• On discretization of the Euler top
• Duffing oscillator and elliptic curve cryptography