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A fast blow-up solution and degenerate pinching arising in an anisotropic crystalline motion
On Hamiltonian flows whose orbits are straight lines
1. | Department of Mathematics, The University of Texas at Austin, Austin, TX 78712 |
2. | Department of Applied Mathematics, University of Colorado, Boulder, CO 80309-0526, United States |
References:
[1] |
A. Dragt and D. Abell, Jolt factorization of symplectic maps, Int. J. Mod. Phys. A (Proc. Suppl.) B, 2 (1993), 1019-1021. |
[2] |
M. de Bondt, Quasi-translations and counterexamples to the homogeneous dependence problem, Proc. Amer. Math. Soc., 134 (2006), 2849-2856.
doi: 10.1090/S0002-9939-06-08335-3. |
[3] |
M. d. Bondt and A. v. d. Essen, Singular Hessians, J. Algebra, 282 (2004), 195-204.
doi: 10.1016/j.jalgebra.2004.08.026. |
[4] |
A. J. Dragt and J. M. Finn, Lie series and invariant functions for analytic symplectic maps, J. Mathematical Phys., 17 (1976), 2215-2227.
doi: 10.1063/1.522868. |
[5] |
É. Forest, Geometric integration for particle accelerators, J. Phys. A, 39 (2006), 5321-5377.
doi: 10.1088/0305-4470/39/19/S03. |
[6] |
K. F. and D. Wang, Variations on a theme by Euler, J. Comput. Math., 16 (1998), 97-106. |
[7] |
S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Pure and Applied Mathematics, 80. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. |
[8] |
H. W. E. Jung, Über ganze birationale Transformationen der Ebene, J. Reine Angew. Math., 184 (1942), 161-174. |
[9] |
H. E. Lomelí, Symplectic homogeneous diffeomorphisms, Cremona maps and the jolt representation, Nonlinearity, 18 (2005), 1065-1071.
doi: 10.1088/0951-7715/18/3/008. |
[10] |
R. I. McLachlan, H. Z. Munthe-Kaas, G. R. W. Quispel and A. Zanna, Explicit volume-preserving splitting methods for linear and quadratic divergence-free vector fields, Found. Comput. Math., 8 (2008), 335-355.
doi: 10.1007/s10208-007-9009-6. |
[11] |
J. Moser, On quadratic symplectic mappings, Mathematische Zeitschrift, 216 (1994), 417-430.
doi: 10.1007/BF02572331. |
show all references
References:
[1] |
A. Dragt and D. Abell, Jolt factorization of symplectic maps, Int. J. Mod. Phys. A (Proc. Suppl.) B, 2 (1993), 1019-1021. |
[2] |
M. de Bondt, Quasi-translations and counterexamples to the homogeneous dependence problem, Proc. Amer. Math. Soc., 134 (2006), 2849-2856.
doi: 10.1090/S0002-9939-06-08335-3. |
[3] |
M. d. Bondt and A. v. d. Essen, Singular Hessians, J. Algebra, 282 (2004), 195-204.
doi: 10.1016/j.jalgebra.2004.08.026. |
[4] |
A. J. Dragt and J. M. Finn, Lie series and invariant functions for analytic symplectic maps, J. Mathematical Phys., 17 (1976), 2215-2227.
doi: 10.1063/1.522868. |
[5] |
É. Forest, Geometric integration for particle accelerators, J. Phys. A, 39 (2006), 5321-5377.
doi: 10.1088/0305-4470/39/19/S03. |
[6] |
K. F. and D. Wang, Variations on a theme by Euler, J. Comput. Math., 16 (1998), 97-106. |
[7] |
S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Pure and Applied Mathematics, 80. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. |
[8] |
H. W. E. Jung, Über ganze birationale Transformationen der Ebene, J. Reine Angew. Math., 184 (1942), 161-174. |
[9] |
H. E. Lomelí, Symplectic homogeneous diffeomorphisms, Cremona maps and the jolt representation, Nonlinearity, 18 (2005), 1065-1071.
doi: 10.1088/0951-7715/18/3/008. |
[10] |
R. I. McLachlan, H. Z. Munthe-Kaas, G. R. W. Quispel and A. Zanna, Explicit volume-preserving splitting methods for linear and quadratic divergence-free vector fields, Found. Comput. Math., 8 (2008), 335-355.
doi: 10.1007/s10208-007-9009-6. |
[11] |
J. Moser, On quadratic symplectic mappings, Mathematische Zeitschrift, 216 (1994), 417-430.
doi: 10.1007/BF02572331. |
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