Research interests
I am keenly interested in symplectic geometry and its numerical applications to Hamiltonian dynamical systems and celestial mechanics, with a particular focus on three- and four-body problems. Besides classical computational methods associated to the study of periodic orbits (continuation method, predictor-corrector algorithm, stability index), I explore Conley–Zehnder index, Krein signature and their interactions at bifurcation points. Why? The Conley–Zehnder index measures a winding number of the linearized flow along a non-degenerate periodic orbit. At bifurcation points the index jumps. When working locally near a family of non-degenerate periodic orbits, there is a fascinating topological bifurcation invariant: the local Floer homology (graded by Conley–Zehnder index) and thus its Euler characteristic. Therefore, the Conley–Zehnder index provides important information how different periodic orbit families are linked to each other at branch points.
My goal is not only to solve specific problems, but also to form a method pool capturing their essential and fundamental features.
Publications
A) By Journal's Editors selected articles
Studying network of symmetric periodic orbit families of the Hill problem via symplectic invariants (with Alexander Batkhin)
Celestial Mechanics and Dynamical Astronomy 137(12) (2025)
https://doi.org/10.1007/s10569-025-10241-7
The Journal CM&DA has started an Astronomy Seminar series organized by Springer Nature. This series consists of a selection of high-quality research on cutting-edge problems in Celestial Mechanics and Dynamical Astronomy. For each seminar, a committee formed by the Journal's editors selects recent paper accepted for publication in CM&DA as being innovative and/or having had significant recent impact. Our article was selected by the committee for the Seminar on Sept. 12, 2025.From Babylonian lunar observations to Floquet multipliers and Conley–Zehnder indices
Journal of Mathematical Physics 64(8) (2023)
https://doi.org/10.1063/5.0156959
One of Hill's main contributions to celestial mechanics was his discovery of a periodic solution with a period of one synodic month of our Moon in his modification of the circular restricted three-body problem. For the analysis of the anomalistic month, Hill used power series and transformed his equations to an infinite set of homogeneous linear equations, at an infinite determinant. Same approach was used by Adams to describe the draconitic month. In contrast to the computational approach by Hill and Adams, in my article I demonstrate in a geometrical way how to use Conley–Zehnder indices and Floquet multipliers of Hill’s lunar orbit to compute numerically the anomalistic and draconitic months. This paper was selected as Editor’s Pick for August 2023 in the Journal of Mathematical Physics.
B) Journal article
Studying network of symmetric periodic orbit families of the Hill problem via symplectic invariants (with Alexander Batkhin)
Celestial Mechanics and Dynamical Astronomy 137(12) (2025)
https://doi.org/10.1007/s10569-025-10241-7Contact geometry of Hill's approximation in a spatial restricted four-body problem
Arnold Mathematical Journal 11(1) (2025)
https://doi.org/10.56994/ARMJ.011.001.005Bifurcation graphs for the CR3BP via Symplectic Methods (with Agustin Moreno, Otto van Koert, Urs Frauenfelder, Dayung Koh)
The Journal of the Astronautical Sciences 71(51) (2024)
https://doi.org/10.1007/s40295-024-00462-7From Babylonian lunar observations to Floquet multipliers and Conley–Zehnder indices
Journal of Mathematical Physics 64(8) (2023)
https://doi.org/10.1063/5.0156959Symplectic splitting of Hamiltonian structures and reduced monodromy matrices
Linear Algebra and its Applications 674, 426–441 (2023)
https://doi.org/10.1016/j.laa.2023.06.008The Conley–Zehnder indices of the spatial Hill three-body problem
Celestial Mechanics and Dynamical Astronomy 135(32) (2023)
https://doi.org/10.1007/s10569-023-10134-7The linear symmetries of Hill's lunar problem
Archiv der Mathematik 120(3), 321–330 (2023)
https://doi.org/10.1007/s00013-022-01822-1
C) Preprint (Submitted for publication)
Exploration of vertical self-resonant bifurcations from DRO in the Earth-Moon CR3BP
https://arxiv.org/abs/2508.17286 (2025)
D) Conference paper / extended abstract
Network of families of symmetric spatial periodic orbits in the Hill problem via symplectic invariants (with Alexander Batkhin)
Book of abstracts of Analytical Methods of Celestial Mechanics 2024Symplectic methods in trajectory design (with Agustin Moreno, Otto van Koert, Urs Frauenfelder, Dayung Koh)
Proceedings of KePASSA 2024Symplectic methods in space mission design (with Urs Frauenfelder, Dayung Koh, Agustin Moreno)
Proceedings of 2023 AAS/AIAA Astrodynamics Specialist Conference
https://arxiv.org/abs/2308.03391v1
E) Doctoral thesis
A study of the Hill three-body problem by modern symplectic geometry
Université de Neuchâtel, No de thèse: 3063 (2023)
https://doi.org/10.35662/unine-thesis-3063
My ORCID profile
ResearchGate profile
Google Scholar profile
arXiv page
Participation in conferences / workshops / summer schools
Symplectic Topology - A conference in honour of Kai Cieliebak
Universität Augsburg, Aug. 24-28, 2026New developments in symplectic geometry
Seoul National University, Nov. 25-28, 2025ISTA Summer School in Dynamical Systems
Bundesinstitut für Erwachsenenbildung (bifeb), Strobl, Sept. 22-26, 2025A stellar afternoon in Symplectic Dynamics (Special guest: James Green, former chief scientist of NASA)
Universität Heidelberg, Nov. 5, 2024Symplectic Dynamics in Aachen
RWTH Aachen, Sept. 16-20, 2024Theories of the three-body system
Monash University Prato Centre, Sept. 8-13, 2024Analytical Methods of Celestial Mechanics 2024 (online participation)
Euler International Mathematical Institute, St. Petersburg, Aug. 19-24, 2024Augsburg Dynamics Days 2024
Universität Augsburg, Aug. 13-14, 2024Symplectic Geometry and Anosov Flows
Internationales Wissenschaftsforum Heidelberg, July 22-26, 202429th International Symposium on Space Flight Dynamics (ISSFD 2024)
Europäisches Raumflugkontrollzentrum (ESOC), Darmstadt, April 22-26, 2024CAST 2024
Ruhr-Universität Bochum, Febr. 8-10, 2024Strasbourg-Heidelberg "Symplectic Day"
IRMA Strasbourg, Nov. 16, 2023Geometry and Dynamics. A Conference in Honour of Leonid Polterovich
ETH Zürich, June 26-30, 2023Two days in Symplectic Dynamics
École normale supérieure de Lyon, Sept. 29-30, 2022Online Miniworkshop on Symplectic and Contact Dynamics
University of Antwerp, May 12, 2021Conservative Dynamics and its Interactions
École Polytechnique Fédérale de Lausanne, Aug. 19-30, 2019Conference in honor of Prof. André Haefliger's 90th birthday
Université de Genève, May 15-17, 2019Workshop on Symplectic Field Theory IX
Universität Augsburg, Aug. 25-31, 2018
Talks
"t.b.a."
Symplectic Topology - A conference in honour of Kai Cieliebak, Universität Augsburg | Aug. 24-28, 2026"Applications of Conley-Zehnder Index to periodic orbits in the Hill problem"
New developments in symplectic geometry, Seoul National University | Nov. 28, 2025"Studying network of symmetric periodic orbit families of the Hill problem via symplectic invariants"
ISTA Summer School in Dynamical Systems, Bundesinstitut für Erwachsenenbildung (bifeb), Strobl | Sept. 23, 2025"Studying network of symmetric periodic orbit families of the Hill problem via symplectic invariants" (online, joint with Alexander Batkhin)
Astronomy Seminars, Research Seminars by Springer Nature, associated to the Journal CM&DA | Sept. 12, 2025"On Research related to CR3BP"
Symplectic Geometry Seminar, Universität Heidelberg | May 28, 2025"Studying network of symmetric periodic orbit families of the Hill problem via symplectic invariants"
Oberseminar Differentialgeometrie, Universität Augsburg | May 19, 2025"Studying network of symmetric periodic orbit families of the Hill problem via symplectic invariants" (online)
Online symplectic/contact geometry seminar, Kongju National University| Febr. 3, 2025"Research activity related to the 3BP"
Europäisches Raumflugkontrollzentrum (ESOC), Mission Analysis Seminar, Darmstadt | Jan. 15, 2025"Studying network of symmetric periodic orbit families of the Hill problem via symplectic invariants"
Science Coffee, Advanced Concepts Team of ESA, ESTEC, Noordwijk | Dec. 13, 2024"Studying network of symmetric periodic orbit families of the Hill problem via symplectic invariants"
A stellar afternoon in Symplectic Dynamics, Universität Heidelberg (Special guest: James Green, former chief scientist of NASA) | Nov. 5, 2024"Application of symplectic invariants to the Hill three-body problem: Bifurcation graphs and Conley–Zehnder indices"
Theories of the three-body system, Monash University Prato Centre | Sept. 13, 2024"Network of families of symmetric spatial periodic orbits in the Hill problem via symplectic invariants" (online, joint with Alexander Batkhin)
Analytical Methods of Celestial Mechanics 2024, Euler International Mathematical Institute, St. Petersburg | Aug. 20, 2024"Contact geometry of Hill's approximation to a spatial restricted four-body problem"
Symplectic Geometry Seminar, Universität Heidelberg | July 3, 2024"On Babylonian lunar periods and Conley–Zehnder indices of the CR3BP"
Symplectic Geometry Seminar, Universität Heidelberg | Nov. 8, 2023