Marian Gidea
Professor of Mathematics
Northeastern Illinois University
Chicago, Illinois

Contact Information: 

Department of Mathematics
5500 N St Louis Ave
Chicago, IL 60605, USA
Phone: 773-442-5779
Fax: 773-442-5770
Email: mgidea at neiu.edu
Office: BBH-204D  

Teaching:

• Year 2011-2012, on leave at the Institute of Advanced Study, Princeton.

Research:

• Dynamical Systems, Chaos Theory, Celestial Mechanics, and applications to mathematical physics, astrodynamics, mathematical biology, and financial mathematics.

CV:

• My current CV.

Editorial boards:

• Associate Editor  of Communications in Nonlinear Science and Numerical Simulation.
• Member of the Editorial Board of Discrete and Continuous Dynamical Systems - S.
• Advisory Editorial Member of Lecture Notes on Nonlinear Physical Science, China Higher Education Publishing and Springer.
• Member of the Editorial Board of Transactions of Nonlinear Science and Complexity,World Scientific.

---

Publications:

Books:

• K. Burns and M. Gidea. Differential Geometry and Topology: with a view to dynamical systems. CRC Press, 2005.
• M. Gidea and C.P. Niculescu. Chaotic Dynamical Systems: An Introduction. Universitaria Press, Craiova, Romania, 2003.

Edited volumes:

• A. Sahin, I. Ugarcovici, M. Gidea (Eds.). Smooth Dynamics, Symbolic Dynamics and Ergodic Theory. Discrete and Continuous Dynamical Systems - S, Vol 2, 2009.
• M.Gidea and J. Masdemont (Eds.). Special Section in Celestial Mechanics and Dynamical Astronomy: Methods and Applications. Communications in Nonlinear Science and Numerical Simulation, Vol. 14, 2009. 
• M. Gidea, E. Perez-Chavela, and C. Robinson (Eds.). A special issue in honor of the contributions of Donald Saari to the mathematical aspects of Celestial Mechanics. Discrete and Continuous Dynamical Systems - S, Vol. 1, 2008.
• M. Gidea, and  C. Robinson (Eds.).  Topological and Analytical Shadowing Techniques. Discrete and Continuous Dynamical Systems - A, Vol. 14, 2006.

Articles:

• M. Gidea and C. Robinson. Diffusion along transition chains of invariant tori and Aubry-Mather sets. Ergodic Theory and Dynamical Systems,  provisionally accepted.
• A. Delshams, M. Gidea, and P. Roldan. Transition map and shadowing lemma for normally hyperbolic invariant manifolds. Discrete and Continuous Dynamical Systems-A, to appear.  
• E. Belbruno, M. Gidea, and F. Topputo. Geometry of Weak Stability Boundaries. Qualitative Theory of Dynamical Systems, submitted.
• M. Gidea, C. Gidea and W. Byrd. Deterministic models for simulating electrocardiographic signals. Communications in Nonlinear Science and Numerical Simulation,  doi:10.1016/j.cnsns.2011.01.022, 2011.
• M. Gidea, J.D. Meiss, I. Ugarcovici, and H. Weiss. Applications of KAM Theory to Population Dynamics. Journal of Biological Dynamics, Vol. 5, 2011, 2010.
• M. Gidea and J. Llibre. Symmetric planar central configurations of five bodies: Euler  plus two. Celestial Mechanics and Dynamical Astronomy, Vol. 106, 2010.
• E. Belbruno, M. Gidea, and F. Topputo. Weak Stability Boundary and Invariant Manifolds. SIAM Journal on Applied Dynamical Systems, Vol. 9, 2010.
• M. Gidea and C. Robinson. Obstruction argument for transition chains of tori interspersed with gaps. Discrete and Continuous Dynamical Systems-S, Vol 2, 2009.
• A. Delshams, M. Gidea, R. de la Llave, T. Seara. Geometric approaches to the problem of instability in Hamiltonian systems. An informal presentation. In Hamiltonian dynamical systems and applications (Eds. W. Craig), Springer, 2008.
• E. Belbruno, M. Gidea and F. Topputo. Resonant Motion, Ballistic Escape, and their Applications in Astrodynamics. Advances in Space Research,  Vol. 42, 2008.
• E. Belbruno, M. Gidea and F. Topputo. Resonance Transitions Associated to Weak Capture in the Restricted Three-Body Problem. Advances in Space Research, Vol. 42, 2008.
• M. Gidea.  Topological methods. In  Advanced Course on Stability and Instability in Mechanical Systems, Quaderns, Vol. 51, Centre de Recerca Matematica, Barcelona, 2008.
• M. Gidea and C. Robinson. Shadowing orbits for transition chains of invariant tori alternating with  gaps. Nonlinearity, Vol. 20. 2007.
• M. Gidea, F. Deppe and G. Anderson. Phase space reconstruction in the restricted three-body problem. In New Trends in Astrodynamics and Applications III (Eds. E. Belbruno), AIP Conference Proceedings Volume 886. 2007.
• M. Gidea and J. Masdemont. Geometry of homoclinic connections in a planar circular restricted three-body problem. International Journal of Bifurcation and Chaos, Vol. 17, 2007
• M. Gidea and F. Deppe. Chaotic orbits in a restricted three-body problem: numerical experiments and heuristics. Communications in Nonlinear Science and Numerical Simulation,  Vol. 11, 2006.
• M. Gidea and R. de la Llave. Topological methods in the large gap problem. Discrete and Continuous Dynamical Systems, Vol. 14, 2006.
• M. Gidea and D. Quaid. On Wesner's method of searching for chaos on low frequency. Economics Bulletin, Vol. 3, 2005.
• M. Gidea and P. Zgliczynski. Covering relations for multidimensional dynamical systems. Journal of Differential Equations, Vol. 202, 2004.
• M. Gidea and P. Zgliczynski. Covering relations for multidimensional dynamical systems - II.  Journal of Differential Equations, Vol. 202, 2004.
• M. Gidea and C. Robinson. Symbolic Dynamics and Transition Tori-II. In New Advances in Celestial Mechanics and Hamiltonian Systems (Eds. J. Delgado, E.A. Lacomba, J. Llibre and E. Perez Chavela), Kluwer Academic/Plenum Publishers, 2004.
• M. Gidea and C. Robinson. Topologically Crossing Heteroclinic Connections to Invariant Tori. Journal of Differential Equations, Vol. 193, 2003.
• M. Gidea and M. Burgos. Chaotic Orbits in Three- and Four-Body Systems. Physica A, Vol. 328, 2003.    
• M. Gidea. Chaotic Julia Sets: A Conley Index Approach. Topology and its Applications, Vol. 125,  2001.
• M. Gidea. Non-smooth Dynamical Systems that Exhibit Hyperbolic Behavior. Revue Roumaine de Mathematiques Pures et Appliques, vol. 45, no. 4, 2000.
• M. Gidea. Leray Functor and Orbital Conley Index for Non-Invariant sets. Discrete and Continuous Dynamical Systems, vol. 5, no. 3, 1999.
• M. Gidea. The Conley Index for Countable Decompositions of Invariant Sets. In Conley Index Theory, Banach Center Publications, vol. 47, Polish Academy of Sciences, 1999.
• M. Gidea.  A Discrete Conley Index for Non-Invariant Sets. In Proceedings of the Topological Methods in Differential Equations and Dynamical Systems Conference, Krakow, Poland, July 17-20, 1996, Universitatis Jagellonicae Acta Mathematica,  fasciculus XXXVI. 1998.
• M. Gidea. Markov partitions for non-hyperbolic systems. Dynamic Systems and Applications, Vol. 5, no. 4, 1996.
• M. Gidea. Stability of the Topological Entropy for a Class of Iterations of Rational Functions with Perturbations. Mathematical Reports, Vol. 32, 1995.

Updated