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Differential dynamical systems
- J. Meiss
- Computer Science, MathematicsMathematical modeling and computation
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
- 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
Abstract We develop a theory of transport in Hamiltonian systems in the context of iteration of area-preserving maps. Invariant closed curves present complete barriers to transport, but in regions…
Targeting chaotic orbits to the Moon through recurrence
Abstract Transport times for a chaotic system are highly sensitive to initial conditions and parameter values. In a previous paper, we presented a technique to find rough orbits (epsilon chains) that…
Markov tree model of transport in area-preserving maps
The survival probability distribution is shown to decay asymptotically as a power law and the decay exponent agrees reasonably well with the computations of Karney and of Chirikov and Shepelyanski.
- J. Meiss
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,…
Periodic orbits for reversible, symplectic mappings
Abstract A 2 N -dimensional symplectic mapping which satisfies the twist condition is obtained from a Lagrangian generating function F ( q , q ′) . The q 's are assumed to be angle variables.…
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…
Applications of KAM theory to population dynamics
- Marian Gidea, J. Meiss, Ilie Ugarcovici, H. Weiss
- Mathematics, MedicineJournal 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.