6 citations · 11 across the 6 of their papers we have counts for
6 papers
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 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…