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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…