6 citations · 19 across the 8 of their papers we have counts for
9 papers
Construction of Approximate Invariants Across Nonlinear Resonances
Yongjun Li, Derong Xu, Yue Hao +1
Our previous work [Y.~Li, D.~Xu, and Y.~Hao, Phys. Rev. Accel. Beams \textbf{28}, 074001 (2025)] introduced a square-matrix method for constructing approximate invariants recursive…
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…
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…
Isochronous and period-doubling diagrams for symplectic maps of the plane
Tim Zolkin, Sergei Nagaitsev, Ivan Morozov +2
Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective vis…
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…
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…
Machine-assisted discovery of integrable symplectic mappings
Timofey Zolkin, Yaroslav Kharkov, Sergei Nagaitsev
We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved q…