2 citations · 2 across the 2 of their papers we have counts for
7 papers
Geometry of Almost-Conserved Quantities in Symplectic Maps. Part III: Approximate Invariants in Nonlinear Accelerator Systems
Tim Zolkin, Sergei Nagaitsev, Ivan Morozov +1
We present a perturbative method for constructing approximate invariants of motion directly from the equations of discrete-time symplectic systems. This framework offers a natural…
Dynamics of McMillan mappings III. Symmetric map with mixed nonlinearity
Tim Zolkin, Sergei Nagaitsev, Ivan Morozov +1
This article extends the study of the dynamical properties of the symmetric McMillan map, emphasizing its utility in understanding and modeling complex nonlinear systems. Although…
Geometry of Almost-Conserved Quantities in Symplectic Maps. Part II: Recovery of approximate invariant
Tim Zolkin, Sergei Nagaitsev, Ivan Morozov +1
Noether's theorem, which connects continuous symmetries to exact conservation laws, remains one of the most fundamental principles in physics and dynamical systems. In this work, w…
Geometry of Almost-Conserved Quantities in Symplectic Maps. Part I: Perturbation Theory
Tim Zolkin, Sergei Nagaitsev, Ivan Morozov +1
Noether's theorem, which connects continuous symmetries to exact conservation laws, remains one of the most fundamental principles in physics and dynamical systems. In this work, w…
Dynamics of McMillan mappings II. Axially symmetric map
Tim Zolkin, Brandon Cathey, Sergei Nagaitsev
In this article, we investigate the transverse dynamics of a single particle in a model integrable accelerator lattice, based on a McMillan axially-symmetric electron lens. Althoug…
Dynamics of McMillan mappings I. McMillan multipoles
Tim Zolkin, Sergei Nagaitsev, Ivan Morozov
In this article, we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings, originally proposed by Edwin McMillan. Both represent the simplest symm…