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Thèmes scientifiques
Je m'intéresse plus particulièrement aux notions suivantes:
- Systèmes dynamiques. Théorie ergodique. Dynamique Symbolique.
- Isométries par morceaux. Billard.
- Pavages.
- Combinatoire des mots.
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Tous les articles sont accessibles sur Arxiv.
Articles publiés.
- Directional billiard complexity in rational polyhedra.Regular and chaotic dynamical systems. 2003, volume 8, numéro 1, pages 97-104.
- Billiard complexity in the hypercube. N.Bedaride & P.Hubert. Annales de l'institut Fourier. 2007, tome 57, numéro 3, pages 719-738.
- Topological entropy of polyhedral billiard. Discrete and continuous dynamical systems. 2007, volume 19, numéro 1, pages 89-102.
- Classification of rotations on the torus T2. Theoretical Computer science. 2007, volume 385, issues 1-3, pages 214-225.
- Periodic trajectories in polyhedral billiard. Forum geometricorum. 2008 Volume 8, pages 107-120.
- Combinatoire du billard. 15pp. Séminaire de théorie spectrale et géométrie 2008.
- Directional complexity of the hypercubic billiard. Discrete mathematics. 2009 Volume 309, pp. 2053-2066.
- Number of balanced words for a given length and height. N. Bédaride & E. Domenjoud, D. Jamet, J.L. Remy (LORIA, Nancy). Discrete mathematics and theoretical computer sciences. 2010, volume 3, 41-62.
- Outer billiard outside regular polygons. N. Bédaride & J. Cassaigne (IML, Marseille).Journal of the London Mathematical Society. 2011, Numero 83 volume 2, 301-323.
- Characterization of quasi-rational polygons. N. Bédaride. Nonlinearity 25 (2012) 3099-3110.
- Geometric realizations of substitutive tilings. N. Bédaride & A. Hilion. Quarterly Journal of Mathematics. 2013 Volume 4, 255-279.
- Minoration of complexity function associated to translations on the torus. N. Bédaride & J.F. Bertazzon. Monatshefte fur Mathematik. 2013 Volume 171, Issue 3, Page 291-304.
- Regular simplex and periodic billiard orbits. N.Bédaride & M. Rao. Proceedings of the American Mathematical Society. 2014, Volume 142 (10),pages: 3511-3519.
- When periodicities enforce aperiodicity. N. Bédaride & Th. Fernique (LIPN, Paris). Communication in Mathematical Physics. 2015 Volume 335, Issue 3, Page 1099-1120.
- No weak local rules for the 4p-fold tilings. N.Bédaride & Th. Fernique. 14pp. Discrete and computational geometry. 2015 Volume 54, Issue 4, Page 980-992.
- An example of PET. Computation of the Hausdorff dimension. N. Bédaride& J.F. Bertazzon. Transactions of the AMS. To appear 39pp.
- Weak local rules for planar octagonal tilings. N. Bédaride& Th. Fernique. Israel Journal of Mathematics. To appear 25pp.
- * Topological substitution and Rauzy fractal. N.Bédaride & A. Hilion & T. Jolivet. Bulletin de la SMF. Ti appear 29pp.
Articles soumis
- Symbolic dynamics for the piecewise rotations: Case of the bijective symmetric maps. N. Bédaride & I. Kaboré. 20pp.
- Thermodynamic formalism and substitutions. N. Bédaride& P. Hubert& R. Leplaideur. 44pp.
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Articles en cours.
- Invariant measures for train track towers. N. Bédaride& A. Hilion& M. Lustig. 50pp.
- Symbolic dynamics for the piecewise rotations: Case of the non-bijective maps. N. Bédaride & I. Kaboré.
- Cohomology and cut and project tilings. N. Bédaride & A. G. Lecuona.
Autres travaux.
Thèse de mathématiques: Étude du billard dans un polyèdre. 27 mai 2005. Institut de Mathématiques de Luminy.
Habilitation à diriger des recherches: Substitutions et isométries par morceaux. 04 novembre 2014. Institut de Mathématiques de Marseille.