• Publications
  • Influence
Differential dynamical systems
  • J. Meiss
  • Computer Science, Mathematics
    Mathematical modeling and computation
  • 2007
TLDR
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
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
TLDR
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.
Symplectic maps
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
TLDR
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.
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