March 3, 2026

Geometry of almost-conserved quantities in symplectic maps

Key Points

The geometric properties of almost-conserved quantities are outlined in the context of symplectic maps, emphasizing their significance in Hamiltonian dynamics.
Specific relationships between these quantities in phase space illustrate their near-conservation and stability behavior over time.
Observational analysis focusing on phase space transformations reveals unexpected structure related to these quantities.
Insights gained elucidate the implications of these geometric aspects across broader Hamiltonian systems.

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Authors

Tim Zolkin

Oldham Council

Sergei Nagaitsev

Fermi National Accelerator Laboratory

I. Morozov

Institute of Catalysis and Petrochemistry

Journals

Chaos Solitons & Fractals

Actions

Institutions

University of Chicago

Brookhaven National Laboratory

Old Dominion University

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Zolkin et al. (Tue,) studied this question.

synapsesocial.com/papers/69a761ccc6e9836116a2fdec — DOI: https://doi.org/10.1016/j.chaos.2026.118059

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The applicability of the third integral of motion: Some numerical experiments· 1964 · 2,047 citations
Fidelity and Reversibility in the Three Body Problem· 2016 · 15 citations
Behavior of Hamiltonian systems close to integrable· 1971 · 75 citations

Also consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Noether's theorem in classical mechanics revisited· 2006 · 23 citations
PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN· 1963 · 937 citations
The applicability of the third integral of motion: Some numerical experiments· 1964 · 2,047 citations
Fidelity and Reversibility in the Three Body Problem· 2016 · 15 citations
Behavior of Hamiltonian systems close to integrable· 1971 · 75 citations

Geometry of almost-conserved quantities in symplectic maps

Key Points

Citation Network

Connected Papers

Discussion

Authors

Journals

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

Cite this study

Also consider

Also consider