PREPRINTS & WORKING PAPERS
5. ''Periodic orbit and KAM Tori on the Planetary N-Body Problem'', F. Crespo, J. Palacián, P. Yanguas and E. A. Turner, (in progress).
4. ''A Novel Approach for Relative Equilibria Configurations in the Full N-Body Problem'', F. Crespo and H. R. Dullin, (in progress).
3. ''Invariant Averaging Theory'', F. Crespo, J. C. van der Meer, J. Vidarte and J. Villafañe, submitted (2025).
2. ''Alternative strategy in Keplerian systems via Melnikov Method. The Lunar Problem as a benchmark'', M. Uribe, E. Martínez and F. Crespo, submitted (2025).
1. ''Examples of b-Poisson Singular Geometries from Celestial Mechanics'', F. Crespo, E. A. Turner, and J. C. van der Meer, submitted (2025).
PUBLISHED
33. E. A. Turner, F. Crespo, "et all" "Stability, Periodic Orbits and KAM Tori in the Dynamics of the Three Fixed Centers Problem",Journal of Dynamics and Differential Equations (2025). Paper
32. F. Crespo, Jhon Vidarte, "et all" "Geometric Numerical Test via Collective Integrators: A Tool for Orbital and Attitude Propagation", Symmetry (2025). Paper
31. E. A. Turner, F. Crespo, J. Sardanyés and N. Morales, ''Quasispecies Dynamics with Time Lags and Periodic Fluctuations in Replication'', Journal of Mathematical Biology (2025). Paper
30. F. Crespo and J. L. Zapata, ''Integrability and periodic orbits in the generalized quasispecies model'', Utilitas Mathematica (2025). Paper
29. F. Crespo, M. Uribe, and E. Martínez, ''Melnikov Method for Perturbed Completely Integrable Systems'', Bulletin of the Belgian Mathematical Society, 32 (1), 45-66 (2025). Paper
28 . F. Crespo, J. Vidarte and J. Villafañe, ''Symplectic Reeb Atlas and Determination of Periodic Solutions in Perturbed Isotropic n-Oscillators'', Journal of Mathematical Analysis and Applications (2024). Paper
27. F. Crespo, F. J. Molero and S. Ferrer "The Elliptope and Bounds in the Rotational Dynamics of Rigid Bodies" Geometric Mechanics (2024). Paper
26. F. Crespo, D.E. Espejo, J. C. van der Meer,'' R^3xSO(3)xT^6-Reduction, relative equilibria, and bifurcations for the full averaged model of two interacting rigid bodies", SIAM Journal on Applied Dynamical Systems (2024). Paper
25. J. Andrade, S. Boatto, F. Crespo, D.E. Espejo, ''On the Stability of Ring Relative Equilibrium in the N-body Problem on S2 with Hodge Potential'', Canadian Journal of Mathematics (2023). Paper
24. F. Crespo, J.L. Zapata and J. Villafañe '' Weierstrass Elliptic Functions from a Dynamical Point of View'', Mathematics in Science, Engineering, and Aerospace (MESA) (2023). Paper
23. F. Crespo and E. Turner, '' Poisson Structure and Reduction by Stages of the Full Gravitational N-Body Problem'', SIAM Journal on Applied Dynamical Systems (2022). Paper
22. J.L. Zapata, E. Martínez, F. Crespo, ''Modified quasispecies model: the analysis of a periodic therapy'', Journal of Mathematical Biology (2022). Paper
21. F. Crespo, J.L. Zapata, S. Rebollo, ''Addition theorems for Ck real functions and applications
in ordinary differential equations'', Aequationes Mathematicae (2021). Paper
20. S. Ferrer, F. Crespo, ''On Moser’s Regularization of the Kepler System. Positive and Negative Energies'', Canadian Mathematical Bulletin (2020). Paper
19. S. Ferrer, F. Crespo, J.L. Zapata, ''Reduced 4D Oscillators and Orbital Elements in Keplerian Systems. Cushman-Deprit Coordinates'', Celestial Mechanics and Dynamical Astronomy (2020). Paper
18. J. L. Zapata, F. Crespo, S. Ferrer, ''Stability and Bifurcations in Hamiltonian Galactic-Tidal Models'', Dynamical Systems: An International Journal (2020). Paper
17. F. Crespo, ''Bifurcations in the Quasispecies Model for Cancer Growth Dynamics'', Nonlinear Studies, 27 (2), 357-366, (2020). Paper
16. F. Crespo, S. Ferrer, ''Alternative reduction by stages of Keplerian systems. Positive, negative and zero energy'', SIAM Journal on Applied Dynamical Systems (2020). Paper
15. J. Andrade, F. Crespo, P. Martínez and C. Vidal, ''McGehee Blow-Up of the Kepler Problem on Surfaces of Constant Curvature'', Qualitative Theory of Dynamical Systems, 19, 13 (2020). Paper
14. F. Crespo, D. E. Espejo and C. Vidal ''Normalization and Existence of Invariant Ray Solutions of a 2-DOF Autonomous Hamiltonian System with Null Frequencies'', Qualitative Theory of Dynamical Systems 19, 18 (2020). Paper
13. F. Crespo, S. Ferrer, and J.C. van der Meer, ''(SO(3) × T4)-Reduction and relative equilibria for a radial axisymmetric intermediary model for roto-orbital motion'', Journal of Geometry and Physics, 150 (2020). Paper
12. J.L. Zapata, F. Crespo, S. Ferrer, and F.J. Molero, ''Relative equilibria of an intermediary model for the roto-orbital dynamics. The low rotation regime'', Advances in Space Research 64, 1317–1330, (2019). Paper
11. F. Crespo and S. Ferrer, “Roto-orbital dynamics of a triaxial rigid body around a sphere. Relative equilibria and stability”, Advances in Space Research, 61: 2725-2739, (2018). Paper
10. A. Cantero, F. Crespo, and S. Ferrer, “Triaxiality Role in the Spin-Orbit Dynamics of a Rigid Body,” Applied Mathematics and Nonlinear Sciences, 3, 1: 187-208, (2018). Paper
9. S. Ferrer and F. Crespo, “Alternative Angle-Based Approach to the KS-Map. An interpretation through Symmetry”, Journal of Geometric Mechanics, 10, 3: 359-372, (2018). Paper
8. F. Crespo, F. J. Molero, S. Ferrer and D. J. Scheeres, “A Radial Axial-symmetric Intermediary Model for the Roto-orbital Motion,” J. of Astronautical Science, 65: 1-28, (2017). Paper
7. F. J. Molero, F. Crespo and S. Ferrer, “A Note on Reparametrizations of the Euler Equations”, Qual. Theory Dyn. Syst., 16: 453–466, (2017). Paper
6. J. C. van der Meer, F. Crespo, S. Ferrer, “Generalized Hopf Fibration and Geometric SO(3) Reduction of the 4DOF Harmonic Oscillator”, Report on Mathematical Physics , 77, 2, (2016). Paper
5. F. Crespo, F. J. Molero and S. Ferrer, “Poisson and Integrable systems through the Nambu Bracket and its Jacobi Multiplier”, Journal of Geometric Mechanics, 8, 2: 169–178, (2016). Paper
4. S. Ferrer, F. Crespo and F. J. Molero, “On the N-extended Euler System: Generalized Jacobi Elliptic Functions”, Nonlinear Dynamic , 84: 413–435, (2016). Paper
3. F. Crespo, G. Díaz–Toca, S. Ferrer and M. Lara, “Poisson and symplectic reductions of 4−DOF isotropic oscillators. e van der Waals system as benchmark”, Applied Mathematics and Nonlinear Sciences, 1, 2: 473–492, (2016). Paper
2. S. Ferrer, F. Crespo, “On the Extended Euler Systems and the Jacobi and Weierstrass Elliptic Functions”, Journal of Geometric Mechanics, 7, 2: 151-168, (2015). Paper
1. S. Ferrer, F. Crespo, “Parametric Quartic Hamiltonian Model. A Unified Treatment of Classic Integrable Systems”, Journal of Geometric Mechanics, 6, 4: 479-502, (2014). Paper
Ph.D. THESIS
F. Crespo, ''Hopf fibration reduction of a quartic model. Applications to rotational and orbital dynamics'', Ph.D. thesis Universidad de Murcia, 2015. Paper