PUBLICATIONS









 

[96]
 Julia Sabalot-Cuzzubbo, William Lafargue-Dit-Hauret, Michel Rérat, Karine Costuas, Didier Bégué, Jacky Cresson, Generation of Helical States - Breaking of symmetries, Curie's principle and Excited states, ChemPhysChem, 2023, pp.e202200951. ⟨10.1002/cphc.202200951⟩. ⟨hal-04013850⟩
[95]
 Jacky Cresson, Laid Boudjellal, Induced potential in Stochastic Newtonian dynamics, 10.p, 2023.
[94]
 Jacky Cresson, Laurene Hume, Les découpages magiques de Harry Houdini, 2.p, 2023.
[93]
 Jacky Cresson, Marielle Péré, Anna Szafranska, Numerical approach to the identification of fractional differential equations and applications in epidemics, 16.p, 2023.
[92]
 Jacky Cresson, Anna Szafranska, Diffusion equations with spatially dependent coefficients and fractal Cauer-type networks, 12.p, 2023
[91]
 Jacky Cresson, Anna Szafranska, From fractal R-L ladder networks to the diffusion equation, 14.p, 2023
[90]
 Jacky Cresson, Rouba Safi, Mid-point embedding of Hamiltonian systems and variational integrators, 24 p, 2023

[89]
 Jacky Cresson, Rouba Safi, Discrete embedding of Lagrangian/Hamiltonian systems and the Marsden-West approach to variational integrators-the order one case, 10.p, 2023
[88] Etienne Behar, Jacky Cresson, Frederic Pierret, Free rotational dynamics of an homogeneous ellipsoid with a stochastic flattening, Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbadjan Vol. 49, No. 1, 2023, Pages 172-188
https://doi.org/10.30546/2409-4994.2023.49.1.172
[87] Jacky Cresson, Khaled Hariz Belgacem, About the structure of the discrete and continuous Eringen's nonlocal elastica, Mathematics and Mechanics of Solids. 2023;28(6):1437-1462. doi:10.1177/10812865221108094
[86] Jacky Cresson, Khaled Hariz Belgacem, Aziz Hamdouni, Jordy Palafox, Noether's theorem for Hamiltonian systems on time scales, 24.p, 2021
[85] Jacky Cresson, Fernando Jiménez, Sina Ober-Blöbaum, Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations, 43.p, 2021, Journal of Geometric Mechanics
[84] Jacky Cresson, Thierry Lehner, Laurent Nottale, Stochastic modification of Newtonian dynamics and induced potential- application to spiral galaxies and the dark potential, J. Math. Phys. 62, 072702 (2021) https://doi.org/10.1063/5.0037265

[84] Jacky Cresson, Les univers de Conway, Maths Express "Croquons les maths !", CIJM, 2021.
[83] Baptiste Anerot, Jacky Cresson, Khaled Hariz Belgacem, Frederic Pierret, Noether's-type theorems on time scales, J. Math. Phys.61 (11), 113502 (2020)
https://doi.org/10.1063/1.5140201
[82] Jacky Cresson, Juan Viu Sos, On the equality of periods of Kontsevich-Zagier, Journal de Théorie des Nombres de Bordeaux, Vol. 34, No. 2 (2022), pp. 323-343 (22 pages)
[81] Jacky Cresson, Fernando Jiménez, Sina Ober-Blöbaum, Modelling of the convection-diffusion equation through Fractional Restricted Calculus of Variations, IFAC-PapersOnLine, Vol. 54, Issue 9, 2021, Pages 482-487. 
[80] Julia Sabalot-Cuzzubo, Germain Salvato-Vallverdu, Didier Bégué, Jacky Cresson, Relating the molecular topology and local geometry: Haddon's pyramidalization angle and the Gaussian curvature, J. Chem. Phys.  2020 Jun 28;152(24):244310
[79] Damya Souami, Jacky Cresson, Christophe Biernachi, Frederic Pierret,  On the local and global properties of gravitational spheres of influence, Monthly Notices of the Royal Astronomical Society, Volume 496, Issue 4, August 2020, Pages 4287–4297.
[78] Florin Avram, Jacky Cresson, Beyond Wentzell-Freidlin: semi-deterministic approximations for diffusions with small noise and a repulsive critical boundary point, to appear in Monogr. Mat. García Galdeano, Prensas Univ. Zaragoza, Zaragoza, 2020.
[77] Cresson, Jacky; Szafrańska, Anna; About the Noether's theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof. Fract. Calc. Appl. Anal. 22 (2019), no. 4, 871–898.
[76] Cresson, Jacky; Szafrańska, Anna; Comments on various extensions of the Riemann–Liouville fractional derivatives : About the Leibniz and chain rule properties. Commun. Nonlinear Sci. Numer. Simul. 82 (2020)
[75] Cresson, Jacky; Kheloufi, Yasmina; Nachi, Khadra; Pierret, Frederic Selection of a stochastic Landau-Lifshitz equation and the stochastic persistence problem. J. Math. Phys. 60 (2019), no. 8, 083512, 38 pp.
[74] Cresson, Jacky; Kheloufi, Yasmina; Nachi, Khadra A stochastic invariantization method for Itô stochastic perturbations of differential equations. Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb. 45 (2019), no. 1, 75–89.
[73] Cresson, Jacky; Palafox, Jordy Lie algebras and geometric complexity of an isochronous center condition. Fourteenth International Conference Zaragoza-Pau on Mathematics and its Applications, 75–83, Monogr. Mat. García Galdeano, 41, Prensas Univ. Zaragoza, Zaragoza, 2018.
[72] Cresson, Jacky; Palafox, Jordy Isochronous centers of polynomial Hamiltonian systems and a conjecture of Jarque and Villadelprat. J. Differential Equations 266 (2019), no. 9, 5713–5747.
[71] (avec Stefanie SONNER) A note on a derivation method for SDE models: Applications in biology and viability criteria,  Stoch. Anal. Appl. 36 (2018), no. 2, 224–239.
[70] (avec Anna SZAFRANSKA) Discrete and continuous fractional persistence problems -- the positivity property and applications,  Commun. Nonlinear Sci. Numer. Simul. 44 (2017), 424–448.
[69] (avec Frederic PIERRET) Multiscale functions, scale dynamics and applications to partial differential equations,  J. Math. Phys. 57 (2016), no. 5, 053504, 32 pp.
[68] (avec Frederic PIERRET) Nonstandard finite difference scheme preserving dynamical properties.  J. Comput. Appl. Math. 303 (2016), 15–30.
[67] (avec Bénédicte PUIG et Stefanie SONNER) Stochastic models in biology and the invariance problem, Discrete Contin. Dyn. Syst. Ser. B 21 (2016), no. 7, 2145–2168.  
[66] (avec Hugo SANTOS SILVA, Agnès RIVATON, Didier BEGUE, Roger C. HIORNS, Correlating geometry of multidimensional carbon allotropes molecules and stability, Organic Electronics, Vol. 26, November 2015, pp. 395-399.
[65] (avec Frederic PIERRET et Benedicte PUIG) The Sharma-Parthasarathy stochastic two-body problem,  J. Math. Phys. 56 (2015), no. 3, 032701, 21 pp.
[64] Cresson, Jacky; Wiggins, Stephen A λ-lemma for normally hyperbolic invariant manifolds. Regul. Chaotic Dyn. 20 (2015), no. 1, 94–108.
[63] Fractional variational embedding and Lagrangian formulations of dissiaptive partial differential equations, in Fractional Calculus in Analysis, dynamics and optimal control, p.65-127, Nova Publishers, New-York, 2013.
[62] Fractional calculus in Analysis, dynamics and optimal control, Mathematics research developments, J. Cresson editor, Nova Publishers, New York, 2013, 244 pages. livre-nova
[61] (avec Frédéric PIERRET et Bénédicte PUIG) Stochastic perturbation of the two-body problem, SF2A-2013: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics. Eds.: L. Cambresy, F. Martins, E. Nuss, A. Palacios, pp.195-203. pdf
[60] (avec Bénédicte PUIG et Stefanie SONNER) Validating Stochastic Models : Invariance criteria for systems of stochastic differential equations and the selection of a stochastic Hodgkin-Huxley type model, Internat.J.Biomath.Biostat 2 (2013) 111-122. pdf
[59] (avec Loic BOURDIN) Helmholtz's inverse problem of the discrete calculus of variations, Journal of Difference Equations and Applications 19(9):1417-1436, 2013. pdf
[58] (avec Stefanie SONNER et Messoud EFENDIEV) On the positivity of solutions of systems of stochastic PDEs, Zeitschrift für Angewandte Mathematik und Mechanik, Vol 93, Issue 6-7, pages 414-422, June 2013. pdf
[57] (avec Delfim TORRES et Agnieszka MALINOWSKA) Differential, integral and variational time-scales embedding of Lagrangian systems, Computers and Mathematics with Applications Volume 64, Issue 7, October 2012, Pages 2294–2301 pdf
[56] A notion of stochastic characteristics for parabolic and mixed-type PDEs, 12.p, 2011, en révision pdf
[55] (avec Isabelle GREFF et Pierre INIZAN) Lagrangian for the convection-diffusion equation, Mathematical Methods in Applied Sciences 35, 15, 1885--1895, 2012. pdf
[54] (avec Isabelle GREFF et Loic BOURDIN) A discrete/continuous fractional Noether theorem, Communication in Nonlinear Science and Numerical Simulation, 18, 4, 878--887, 2013 pdf
[53] The stochastisation hypothesis and the spacing of Planetary systems, Journal of Mathematical Physics 2011, v. 52 (11), 113502. pdf
[52] Cresson, Jacky; Greff, Isabelle; Pierre, Charles Discrete embeddings for Lagrangian and Hamiltonian systems. Acta Math. Vietnam. 43 (2018), no. 3, 391–413. pdf
[51] (avec Jasmin RAISSY) About the trimmed and the Poincaré-Dulac normal form of diffeomorphisms, Bollettino della Unione Matematica Italiana (9) V (2012), pp. 55--80. pdf
[50] (avec Loic BOURDIN, Isabelle GREFF et Pierre INIZAN) Variational integrators for Fractional Lagrangian systems in the framework of discrete embeddings, 13.p, Applied Numerical Mathematics, Volume 71, September 2013, Pages 14–23.
 pdf
[49] Introduction to embedding of Lagrangian systems, International Journal of Biomathematics and Biostatistics, Vol. 1, no. 1, 23-31, 2010 pdf
[48] (avec Stefanie SONNER et Messoud EFENDIEV) , Necessary and Sufficient Conditions for the Positivity of Solutions of Systems of Stochastic PDEs, soumis pdf
[47] (avec Pierre INIZAN)  , Variational formulations of differential equations and asymmetric fractional embedding, Journal of Mathematical Analysis and Applications 385 (2012) 975–997. pdf
[46] (avec Isabelle GREFF) A non-differentiable Noether theorem, Journal of Mathematical Physics  52 (2011), no. 2, 023513, 10 pp. pdf
[45] (avec Isabelle GREFF) Non-differentiable embedding of Lagrangian systems and PDEs, Journal of Mathematical Analysis and Applications, Volume 384, Issue 2, 15 December 2011, Pages 626-646. pdf
[44] Calcul Moulien, Annales de la Faculté des Sciences de Toulouse Mathématiques Vol. XVIII, no. 2, 2009, pp. 307-395. pdf
[43] Inverse problem of fractional calculus of variations for partial differential equations, Communications in Nonlinear Science and Numerical Simulation, Volume 15, Issue 4, April 2010, Pages 987-996. pdf
[42] (avec Pierre INIZAN) About fractional Hamiltonian systems, Physica Scripta 2009 014007. pdf
[41] (avec Christophe GUILLET) Hyperbolicity versus partial-hyperbolicity and the Transversality-Torsion phenomenon, Journal of Differential equations 244 (2008), 2123-2132 pdf
[40] Dynamique des nombres et Physique des oscillateurs, Journal de Théorie des nombres de Bordeaux 20 (2008), 107-123. pdf
[39] (avec Gastao S. F. FREDERICO et Delfim F. M. TORRES) Constants of Motion for Non-Differentiable Quantum Variational Problems, Topological Methods in Nonlinear Analysis Vol.33, No. 2, June 2009, 217-232. pdf
[38] (avec Aris DANIILIDIS et Masahiro SHIOTA) On the First Integral conjecture of René Thom, Bulletin des Sciences Mathématiques 132 (2008) 625-631. pdf
[37] (avec Sébastien DARSES) Stochastic embedding of dynamical systems, J. Math. Phys. 48, 072703 (2007) (54 pages) pdf
[36] (avec Stéphane FISCHLER et Tanguy RIVOAL) Phénomènes de symétries dans des formes linéaires en polyzêtas, Journal für die reine und angewandte Mathematik (Crelle's Journal), 617 (2008), 109-151. pdf
[35] Fractional embedding of Differential Operators and Lagrangian systems, J. Math. Phys. 48, 033504  (2007) (34 pages) pdf
[34] (avec Stéphane FISCHLER et Tanguy RIVOAL) Séries hypergéométriques multipes et polyzêtas, Bulletin de la Société Mathématique de France, 2007 pdf
[33] (avec S. DARSES) Théorème de Noether Stochastique, C.R. Acad. Sci. Paris, Ser. I 344 (2007) 259-264 pdf
[32] Polyzêtas stricts, larges et pondérés, Publications Mathématiques de Besançon-Algèbre et Théorie des Nombres, 33-41, 2007. pdf
[31] Voyage au coeur des nombres, Repères. Num. 69. p. 95-103., 2007. pdf
[30] Non-differentiable deformations of Rn, International Journal of Geometric Methods in Modern Physics, Vol. 3, no. 7 (2006) 1395-1415. pdf
[29] (avec S. DARSES), Plongement stochastique des systèmes dynamiques, C. R. Acad. Sci. Paris, t. 342, Série I, 333-336, 2006. pdf
[28]
 (avec F. BEN ADDA) Fractional differential equations and the schrödinger equation, Applied Mathematics and Computations, 161, no. 1, 323-345, 2005 pdf
[27] Non differentiable variational principles, Journal of Mathematical Analysis and Applications, Vol. 307, no. 1, 48-64, 2005. pdf
(d) Théorie de Plongement des systèmes dynamiques, Programme de Recherche, 21.p, Mars 2005. pdf
[26] Hyperbolicity, transversality and analytic first integrals, Journal of Differential Equations, 196, 289-300, 2004. pdf
[25] (avec F. BEN ADDA) Quantum derivatives and the schrödinger equation, Chaos, solitons and fractals, Vol. 19, no.5, 1323-1334, 2004. pdf
[24] Symbolic dynamics and Arnold diffusion, Journal of Differential Equations 187, 269-292, 2003. pdf
[23] (avec C. GUILLET) Periodic orbits and Arnold diffusion, Discrete and Continuous Dynamical Systems, Vol. 9, no. 2, 451-469, 2003 [PS]
[22] Scale calculus and the Schrödinger equation, Journal of Mathematical Physics, Vol. 44, no. 12, 32.p, 2003 pdf
[21] Obstruction à la linéarisation des champs de vecteurs polynomiaux, Canadian Mathematical Bulletin, Vol. 45, no.3, 355-363, 2002 pdf
[20] Scale relativity for one dimensional non differentiable manifolds, Chaos, Solitons and Fractals, Vol. 14, no. 4, 553-562, 2002 [PDF]
[19] La relativité d'échelle se confirme, La recherche no. 359, Décembre 2002.
(c) Quelques problèmes de physique-mathématique, 70.p, Mémoire d'Habilitation à Diriger des Recherches, Université de Franche-Comté, Décembre 2001. [PDF]
[18] The transfer lemma for Graff tori and Arnold diffusion time, Discrete and  Continuous Dynamical Systems  Vol. 7, no. 4, 787-800, 2001. [PS]
[17] (avec M. RABIET), Hyperbolicité et non intégrabilité analyttique I. Points hyperboliques, C. R. Acad. Sci. Paris, t. 332, Série I, 325-328, 2001. pdf
[16] Hyperbolicité et non intégrabilité analytique II. Tores normalement et partiellement hyperboliques, C. R. Acad. Sci. Paris, t. 333, Série I, 229-232, 2001. pdf
[15] Temps d'instabilité des systèmes hamiltoniens initialement hyperboliques, C. R. Acad. Sci. Paris, t. 332, Série I, 831-834, 2001. pdf
[14] (avec F. BEN ADDA) About non differentiable functions, Journal of Mathematical Analysis and Applications 262, 721-737, 2001. pdf
[14*] Ben Adda, Fayçal; Cresson, Jacky Corrigendum to "About non-differentiable functions'' [J. Math. Anal. Appl. 263 (2001) 721–737] [MR1866075]. J. Math. Anal. Appl. 408 (2013), no. 1, 409–413. 26A33 pdf
[13] (avec B. SCHUMAN) Formes normales et problème du centre, Bulletin des Sciences Mathématiques 125, no.3, 235-252, 2001. pdf
[12] (avec M. PLANAT), The readout of time, continued fractions and 1/f noise, dans Noise in physical systems and 1/f fluctuations, Proceedings of the 16th International conference Gainesville, Florida, 22-25 october 2001, Edited by Gijs Bosman, World Scientific 2001.
(b) (avec F. BEN ADDA), Calcul Fractionnaire, variétés Fractales et Relativité d'échelle, Prépublication 2000/11  Math. Besançon, 93.p, 2001. [PS]
[11] Hamiltonian chaos, AIP Conf. Proc 517, Dubois ed., 510-525, 2000. [PS]
[10] Dynamique symbolique et tores partiellement hyperboliques, C. R. Acad. Sci. Paris, t. 330, Série I, 1091-1096, 2000 pdf
[9] Un lambda-lemme pour des tores partiellement hyperboliques, C. R. Acad. Sci. Paris, t. 331, Série I, 65-70, 2000. pdf
[8] (avec J-N. DENARIE), Geometry and dynamics of numbers under finite resolution, dans Noise, oscillators and algebraic randomness, Planat ed., Lect. Notes in Physics, 305-323, 2000. [PS]
[7] (avec F. BEN ADDA), Divergence d'échelle et différentiabilité, C. R. Acad. Sci. Paris, t. 330, Série I, 261-264, 2000 pdf
[6] (avec M. PLANAT, S. DOS SANTOS, S. PERRINE, N. RATIER), Close to resonance interaction of radiofrequency waves in a Chottky diode mixer : 1/f noise and number theory, dans Quantum noise and other low frequency fluctuations in electronic devices, AIP Press, P. Handel, A. Chung ed., 177-187, 1999.
[5] (avec M. PLANAT, S. DOS SANTOS, S. PERRINE), 1/f frequency noise in a communication receiver and the Riemann hypothesis, ICNF 1999, 15th International conference on Noise in Physical systems and 1/f fluctuations, 1999.
(a) Systèmes dynamiques, Bruit en 1/f et Théorie des nombres, Programme de Recherche, 32.p, Janvier 1999. [PS]
[4] (avec B. SCHUMAN), Formes normales et problème du centre symétrique, C. R. Acad. Sci. Paris, t. 327, Série I, 581-584, 1998. pdf
[3] Conjecture de Chirikov et optimalité des exposants de stabilité du théorème de Nekhoroshev, Prépublication 98/40 Math. Besançon, 21.p, 1998. [PS]
[2] Instabilité des systèmes hamiltoniens proches intégrables, Thèse de Doctorat, Spécialité Mathématiques, 188.p, Observatoire de Paris, Décembre 1997. [PS]
[1] A lambda-lemma for partially hyperbolic tori and the obstruction property, Letters in Mathematical Physics, Vol. 42, no.4, 363-377, 1997.