LIST    OF    PUBLICATIONS



Articles


A1  M.COURBAGE, S.MIRACLE-SOLE and D.W.ROBINSON :
    Normal States and Representation of the Canonical Commutations Relations, Ann.
    Inst.Henri Poincaré, 14, 171-178, (1971).

A2. M.COURBAGE :
    Opérateur de collision et invariants pour les systèmes quantiques à spectre discret.
    Bull.Cl.Sci Acad Roy Belgique, 61, 715-733, 33, (1975).

A3. M.COURBAGE :
    On the Collision Operator for Quantum Systems with Discrete Spectrum. Physica,
    82 A, 312-318, (1976).

A4. M. COURBAGE :
    Une classe d'invariants réguliers en tant que limites  asymptotiques ou moyennes
    ergodiques. Ann. Inst. Henri Poincaré, 27, 387-405, (1977).

A5. M.COURBAGE :
    Spectral Deformation Techniques Applied to the Study of Quantum Statistical     Irreversible Processes. Lett. Math. Physics, 2, 451-457, (1978).

A6. B.MISRA, I.PRIGOGINE and M. COURBAGE :
    From the Deterministic Dynamics to Probabilistic Descriptions .Proc.Natl.
     Acad.Sci. U.S.A, 76,  3607-3611, (1979).

A7. B.MISRA, I. PRIGOGINE and M. COURBAGE :
    From the Deterministic Dynamics to Probabilistic Descriptions Physica 98 A, 1-26,     (1979).

A8. B. MISRA, I.PRIGOGINE and M. COURBAGE :
    Liapounov Variable, Entropy and Measurement in Quantum Mechanics. Proc.     Natl.Acad. Sci  U.S.A 76, 4768-4772, (1979).

A9. M. COURBAGE and B. MISRA :
    On the Equivalence Between Bernoulli Systems and Stochastic Markov Processes.
    Physica, 104 A, 359-377, (1980).

A10.M. COURBAGE :
    On necessary and Sufficient Conditions for the Existence of Time and Entropy
    Operators in Quantum Mechanics. Lett.Math.Phys.4, 425-432, (1980).

A11. S.GOLDSTEIN, B.MISRA and M. COURBAGE :
    On Intrinsic Randomness of Dynamical Systems. J.Stat.Phys. 25, 11-126, (1981).

A12. M.COURBAGE :
    Mathematical Problems of Irreversible Statistical Mechanics for Quantum     Systems. I : Analytic Continuation of the Collision and Destruction Operators by
    Spectral Deformation Methods. J.Math. Phys. 23, 646-651, (1982).

A13. M.COURBAGE :
    Mathematical Problems of Irreversible Statistical Mechanics for Quantum     Systems. II : On the Singularities of ( ç (z)-z))-1 and the Pseudo-Markovian
    Equation.Application to Lee Model. J.Math.Phys.23, 652-658, (1982).

A14. M.COURBAGE and I.PRIGOGINE :
    Intrinsic Randomness and Intrinsic Irreversibility in Classical Dynamical Systems.
    Proc.Natl. Acad.Sci. U.S.A,  2412-2416, (1983).

A15. M.COURBAGE :
    Intrinsic Irreversibility in Kolmogorov Dynamical Systems. Physica 122A,
    459-482, (1983).

A16. M.COURBAGE :
    Remarks on Non-Equilibrium Correlations in Simple Dynamic Model.Phys.Lett.
    110 A, 77-80, (1985).

A17. M.COURBAGE :
    Remarks on a Recent Article of Ch.Obcemea and E.Brandäs on the Theory of
    Subdynamics.Ann.Phys. 166, 250-252, (1986).

A18. I. ASSANI and M.COURBAGE :
    On the Loss of Information in the Transition from Deterministic Systems to
    Probabilistic Processes. Lett.Math.Phys. 12, 257-265, (1986).

A19. M.COURBAGE, C.COUTSOMITROS and B.MISRA :
    Faithfulness property of the transition from Bernoulli system to irreversible     Markov processes. Physica A, 155, 167-174, (1989).

A20. M.COURBAGE :
    On the approach to statistical equilibrium in infinite lattice dynamic model. J.     Math.Phys. 30, 1840-1850, (1989).

A21. M.COURBAGE and G.NICOLIS :
    Markov Evolution and H-Theorem under Finite Coarse-Graining in Conservative
    Dynamical Systems, Europhysics Letters, 11, 1-6, (1990).

A22. M.COURBAGE and D.HAMDAN :
    A class of non-mixing dynamical systems with monotonic semi-group property.
    Lett.Math.Phys, 22, 101-106, (1991).

A23. M.COURBAGE and D.HAMDAN :
    Non-Markovian reversible invariant measures on the Subshifts of Finite Type.
    J.Stat.Phys. 74, 1281-1292, (1994).

A24. M.COURBAGE and D.HAMDAN :
    Chapman-Komogorov equation for non-Markovian shift invariant measures, Ann .     Prob., 22, 1662-1677, (1994).

A25. M.COURBAGE and D.HAMDAN :
    Unpredictability in some non chaotic dynamical systems. Phys.Rev.Lett. 74, 5166,
    (1995).

A26. M.COURBAGE and D.HAMDAN :
    Decay of Correlations and mixing properties in a dynamical system with zero K-S
    entropy. Ergod Th. and Dynam. Syst. 16, 1-17, (1996).

A27. M.COURBAGE :
On the Abundance of Traveling Waves in Infinite 1-D Cellular Automata . Physica D 103 ,    133-144, (1997).

A28. M.COURBAGE :
    Entropy production and irreversibility in dynamical systems
     Int. J. Theor. Phys. 36, 2209-2220 (1997)

A29.M.COURBAGE and D.HAMDAN :
    An Ergodic Markov Chain is not determined by its Two-dimensional      Marginal Laws , Statistics and Probability Letters,  37, 35-40 (1998)

A 30 M. COURBAGE and B.KAMINSKI :
    On intrinsic weak randomness of Kolmogorov Zd - actions on a Lebesgue space
                   J. Stat. Phys., 97,  781-792,  (1999)

A 31 M. COURBAGE,  D. MERCIER an d S. YASMINEH
                   Travelling waves and chaotic properties in cellular automata
                    CHAOS,  9,  893-901 (1999)

A 32 V. AFRAIMOVICH and M. COURBAGE
      On the abundance of traveling waves in coupled expanding circle maps.
    in : Methods of Qualitative Theory of Differential Equations
             (Trans:AMS)  Series. 2,  vol. 200 , American Mathematical Society,  Providence, RI,     (2000).

A 33  M. COURBAGE and S. YASMINEH
    Wavelengths distributions of chaotic travelling waves in some cellular automata
              Physica D, 150 , 63-83 (2001).              


 
A34  M.COURBAGE and D.HAMDAN :
    Examples of Ergodic Stationary Processes uniquely determined by  Two-    dimensional  Marginal Laws, Statistics and Probability Letters, vol 52/4, 341-345     (2001)

A 35  M. COURBAGE & J.-G. MALHERBE
    Extended  memory processes generated by simple dynamical systems
and scaling behavior of the entropy   "Chaos,  Solitons and Fractals" vol 13/2, 253-260 (2001).
A 36  M. COURBAGE
Time operator in quantum mechanics and some stochastic processes with long memory   Cybernetics and Systems:. International Journal,  vol 32/3-4 , 385-392 (2001).

A 37 M. COURBAGE and D.HAMDAN :
A family of stationary processes with infinite memory  having the same p-marginals . Ergodic and spectral properies. Colloq. Math. Vol. 90, (2001), 159-179.

A 38 B. CAZELLES, M. COURBAGE and M. RABINOVICH
    Anti-phase regularization of coupled chaotic maps modelling bursting neurons     Europhys.  Lett. Vol 56, (2001), 504-509

A 39  Jean-Paul ALLOUCHE, Maurice COURBAGE,  Gencho SKORDEV
Notes on Cellular automata. , Cubo Matematica Educational , vol. 3., n° 2, 213-244, 2001.     

A 40  M . COURBAGE  and B. KAMINSKI
    On the directional entropy of Z2-actions generated by permutative cellular
    automata , Studia Mathematica, vol 153 (3),285-295,  2002.

A 41  M. BERNARDO, M. COURBAGE et T. TRUONG
Random walks generated by area preserving maps with zero Lyapounov exponents, Communications in Nonlinear Science and Numerical Simulations,  8, 189-199  (2003)

A. 42  M. COURBAGE  and B. KAMINSKI :
On intrinsically random Z2-actions on a Lebesgue space : J. Statist. Phys.  112  (2003),  no. 1-2, 421--427.

A. 43  M. COURBAGE  and B. KAMINSKI :
Space-time intrinsic randonness of dynamical systems and statistical mechanics,      Int. J. Quant. Chem., vol 98, 145-149,  (2004)

A 44  M. COURBAGE:
Time in Dynamical Systems,  Discrete Dynamics in Nature and Society, 1, 85-90, (2004)

 A 45  M. BERNARDO, M. COURBAGE et T. TRUONG
Multidimensional Gaussian sums arising from distribution of Birkhoff sums in zero entropy dynamical systems, J. Phys. A,  37, 11759- 11801, (2004)

A 46  M. COURBAGE, V.B. KAZANTSEV, V.I. NEKORKIN, M. SENNERET
Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons, CHAOS, 14, 1148-1156, (2004)

A 47  M. COURBAGE, 
    Semi-groups and time operators for quantum unstable systems,
    To appear in  Int. J. Theor. Phys.(2006) arxiv.org/abs/quant-ph/0410082

A 48 M. COURBAGE and B. KAMINSKI
Space-time directional Lyapounov exponents for cellular automata, To appear in  Journal of Stat. Phys.

A 49 M. COURBAGE et M. SABERI
Computation of Entropy increase in Lorentz gas and hard  disks, To appear in  Communications in Nonlinear Science and Numerical Simulations

PREPRINTS       

P1 M. BERNARDO and M. COURBAGE
    Computation of directional topological entropy for permutative cellular automata
    ( Thèse M. Bernardo, juin 2001, Paris 7, p. 93-122)

P2 M. COURBAGE and B. KAMINSKI
    Density of measure-theoretical directional entropy for lattice dynamical systems

P3 M. COURBAGE , T. DURT and M. SABERI,
    Quantum Decay Laws and Kaon Phenomenology in the Friedrichs Model

PROCEEDINGS

C1. M.COURBAGE :
    Intrinsic Stochasticity and Irreversibility of Classical and Quantum Systems.In
    "Dynamical Systems and Microphysics", Ed.A.Blaquière, F.Fer and A.Marzollo,
    225-232, Springer 1980.

C2. M.COURBAGE :
    Non-Equilibrium Entropy for Kolmogorov Dynamical Systems. In "Dynamical
    Systems and Microphysics "Eds.A.Avez and A.Blaquière. Academic Press,
    415-423, (1982).

C2 bis B. MISRA, I.PRIGOGINE and M. COURBAGE :
    Liapounov Variable, Entropy and Measurement in Quantum Mechanics.
    Reprise de A8 dans l'ouvrage collectif:"Quantum Theory and Measurement"     Eds.J.A. Wheeler and W.Z. Zurek. Princeton University press 1983
       
C3. M.COURBAGE :
    Irreversibility of Dynamical Systems. In : Non-Linear and Turbulent Processes in
    Physics, Vol.3, Ed.R.Z.Sagdeev, Harwood Acad.Publ. (1984),1281-1288.

C4. M.COURBAGE :
    Entropie thermodynamique et information. In "Fractals, dimensions non entières et
    applications". Ed.G.Cherbit, Masson, 316-328, (1987).

C5. M.COURBAGE :
    On the Description of Quantum Dissipative Processes. In : "Information,     Complexity and Control in Quantum Mechanics. Ed.A.Blaquière, S.Diner and
    G.Lochack, CISM, Udine, 241-263, Springer-Verlag, (1987).

C6.M.COURBAGE :
    L'entropie comme sélecteur des conditions initiales. In "Temps et Devenir",     colloque international de Cerisy 1983, ed.E.Brans, I.Stengers et P.Vincke.Patinio,
    Genève (1988), 222-226.

C7. M.COURBAGE:
    Une formulation microscopique du second principe de la thermodynamique :     information et irreversibilité. Annales de la Fondation Louis de Broglie,  13, 489-    512, (1988) (paru également dans les comptes rendus du Séminaire Synergie et     Cohérence, Paris, ed.Z.W.Wolkowski (1988).

C8. M.COURBAGE :
    On Boltzmann entropy and Coarse-graining for a class of dynamical systems.
    Proceedings of the Nato advanced Institute on Information Dynamics, Irsee, RFA
    (1991). Eds H.Atmanspacher et al. Plenum Press, (1991), 237-243.

C9. M.COURBAGE :
    Dynamics and the arrow of time, Proccedings of the Workshop "The Paradigm of
    Self-organization", ed.G.J.Delanoort, Gordon & Breach, London, (1993), 94-110.

C10.M.COURBAGE :
    Unpredictability in determinsitic systems.
    Proceedings of Zakopane (Pologne)  Conference on Non Linear Dynamics,     Chaotic and Complex Systems. J. of Tech Phys. 38, 1985-1988 (1997) .

C11 H.CHATE and M. COURBAGE
    Préface de "Lattice Dynamics"  Physica D,103, N° 1-4, 612 p.  Elsevier (1997)., pages vii-viii

C12. M. COURBAGE :
    Dynamical aspects of processes with long-range memory. In proceedings of
    Generalized functions, operator theory, and dynamical systems (Brussels, 1997),
    361--367, Chapman & Hall/CRC Res. Notes Math., 399,
    Chapman & Hall/CRC, Boca Raton, FL,1999.

C13. M. COURBAGE :
  Time operator in quantum mechanics. Proceedings of the Symposium "Time's Arrow", Vienna, Austrian Soc. For Cybernetic Studies,  202-204, 2000 .

C14  J.G. MALHERBE & M. COURBAGE
             Création et études d'ondes progressives dans les réseaux d'applications couplées, in: Pomeau, Ribotta ed.Comptes rendus de la Rencontre du Nonlinéaire, 271-275,  2000,  Edition Paris 11.

C 15   M. COURBAGE
    Stochastic processes determined or not determined by their 2-dimensional marginal     laws, Proceedings of "Ergodic Theory and Dynamical Systems",36-37,  Nicholas     Copernicus University, Faculty of Math.and Computer Sci. Torun 2001.

C 16   B. CAZELLES,M. COURBAGE et M. RABINOVICH
Synchronisation  en opposition de phase pour des applications chaotiques couplées décrivant des dynamiques neuronales, 6 pages , in: Pomeau, Ribotta ed Comptes rendus de la Rencontre du Nonlinéaire 2001.

C  17  M. COURBAGE
            Travelling waves and space-time chaos in cellular automata and coupled maps lattices, , in : Progress in nonlinear science, Vol. 2 (Nizhny Novgorod, 2001), Nonlinear oscillations, control and information, Nekorkin, Shalfeev ed, , 31-39, RAS, Inst. Appl. Phys., Nizhny Novgorod, 2002.

C. 18  V. AFRAIMOVICH, M. COURBAGE, B. FERNANDEZ and  A. MORANTE :
Directional entropy in Lattice Dynamical Systems, in : Progress in nonlinear science, Vol. 1 (Nizhny Novgorod, 2001), Mathematical Problemes of Nonlinear Dynamics,  Lerman and Shilnikov ed,,  9--30, RAS, Inst. Appl. Phys., Nizhny Novgorod, 2002.

C 19.  B. CAZELLES, M. COURBAGE and M. RABINOVICH
    Anti-Phase Regularization of Coupled Chaotic Maps Modelling Bursting Neurons
        AIP Conf. Proc. 676, 368 (2003) (http://proceedings.aip.org)

C 20   M. COURBAGE
     Complexity of Extended Dynamical Systems , in proceedings of "Chaotic Transport and Complexity in Fluids and Plasma",  Journal of Physics: Conference Series  Volume 7, 2005, 86-93.

C 21   M. COURBAGE 
    Unstable quantum states and time operator, proceedings de XXV International Colloquium on Group Theoretical Methods in Physics, 2-6 August 2004 Cocoyoc, Mexico, 5 pages, IOP Conf. Series  Conference Series Number 185
    p 203-207.2005, Editors: George S. Pogosyan, Luis Edgar Vicent, and Kurt Bernardo Wolf.

C 22  M. COURBAGE
     Notes on Spectral Theory, Mixing and Transport , in - International Summer-School on  « Chaotic Dynamics and Transport in Classical and Quantum Systems » - P. Collet, M. Courbage, S. Metens, A. Neishtadt and G. Zaslavsky editors. Nato Sc. Series,II, vol. 182, Kluwer, 2005, p 15-33

C 23  M. SENNERET et M. COURBAGE, Antisynchronisation et a pparition d’un attracteur chaotique pour deux neurones couplés, Actes de la Rencontre Nonlinéaire , Paris, 2006.
   


       

REVIEW  ARTICLE .

Jean-Paul ALLOUCHE, Maurice COURBAGE, Joseph.P.S. KUNG and Gencho SKORDEV

Cellular automata. .Encyclopedia of Physical Science and Technology, Third Edition, Vol.2 , 2002  , 555- 567, Academic Press   

BOOKS

Mathématiques pour la Physique (avec P. Besnoist-Gueutal). Eyrolles.
Tome I : Intégrale de Lebesgue. Fonctions Analytiques. Espaces normées. (1992).
Tome II : Séries de Fourier. Transformations de Fourier et de Laplace des Fonctions sommables. Distributions et fonctions spéciales. (1992).
Tome III : Espaces de Hilbert. Opérateurs linéaires dans les espaces de Hilbert. (1993).

"Lattice Dynamics"  Physica D,103, N° 1-4, 612 p.  Elsevier (1997).
 Proceedings of the international workshop Lattice Dynamics, Paris , June 1995. 
H.Chaté and M. Courbage  Editeurs.


« Chaotic Dynamics and Transport in Classical and Quantum Systems »
Lectures of Cargèse International Summer-School, August 2003.
P. Collet, M. Courbage, S. Metens, A. Neishtadt and G. Zaslavsky editors. Nato Sc. Series,II, vol. 182, 455 pages, Kluwer, 2005