Differential dynamical systems
- J. Meiss
- MathematicsMathematical modeling and computation
- 2007
This chapter discusses Hamiltonian dynamics, a type of dynamical system that combines linear systems and manifolds and has applications in medicine, physics, and computer graphics.
Symplectic maps, variational principles, and transport
- J. Meiss
- Physics
- 1 July 1992
Symplectic maps are the discrete-time analog of Hamiltonian motion. They arise in many applications including accelerator, chemical, condensed-matter, plasma, and fluid physics. Twist maps correspond…
Transport in Hamiltonian Systems
- R. MacKay, J. Meiss, I. Percival
- PhysicsHamiltonian Dynamical Systems
- 1 August 1984
Symplectic maps
- J. Meiss
- Mathematics
- 2008
Here Dfij = ∂fi/∂zj is the Jacobian matrix of f , J is the Poisson matrix, and I is the n × n identity matrix. Equivalently, Stokes’ theorem can be used to show that the loop action, A[γ] = ∮ γ pdq,…
Converse KAM theory for symplectic twist maps
The authors derive a criterion for the non-existence of invariant Lagrangian graphs for symplectic twist maps of an arbitrary number of degrees of freedom, interpret it geometrically, and apply it to…
Applications of KAM theory to population dynamics
- M. Gidea, J. Meiss, Ilie Ugarcovici, H. Weiss
- BiologyJournal of Biological Dynamics
- 1 January 2011
This work identifies the mechanism that generates extremely complicated orbit structures in population models, including islands-around-islands, ad infinitum, with the smaller islands containing stable periodic points of higher period.
Generating forms for exact volume-preserving maps
We develop a general theory of implicit generating forms for volume-preserving diffeomorphisms on a manifold. Our results generalize the classical formulas for generating functions of symplectic…
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