## Juan Tolosa

#### Professor of Mathematics

Phone: | 609.652.4938 |

Email: | Juan.Tolosa@stockton.edu |

Office: | C-121 |

Website/CV: | www.stockton.edu/~tolosaj |

**BIOGRAPHY**

I came to Stockton University in 1986. From 1984 to 1986 I was a visiting professor at the University of California, Berkeley. From 1972 to 1988 I taught at the Universidad Simón Bolívar, Caracas, Venezuela, first as Adjoint Professor, then Associate Professor, and finally as Professor. From 1971 to 1972 I was Associate Professor at the Institute of Mathematics, Universidad de la República, Montevideo, Uruguay.

**EDUCATION**

Ph D in Mathematics, Patrice Lumumba University (PLU), Moscow, USSR, 1966

Master in Mathematics, PLU, 1966

**AREAS OF EXPERTISE**

Structural stability of dynamical systems, maps of the interval, differential equations with time-lag, mathematical models of infectious diseases.

**COURSES TAUGHT**

Complex Analysis, Real Analysis, Topics in Geometry, Foundations of Mathematics, Linear Algebra, Differential Equations, Calculus I, II, and III, Calculus for the Life Sciences, Mathematics Seminar, Geometry for Teachers, Precalculus, Applied Geometry, Russian I and II

**RESEARCH INTERESTS**

Structural stability of dynamical systems, maps of the interval, differential equations with time-lag, mathematical models of infectious diseases, classical geometry

**PUBLICATIONS**

*An Averaging method for Quasilinear Differential Equations with Retarded Argument and Periodic Coefficients*, Trudy Sem. Teor. Diff. Urav. Otkl. Arg., Patrice Lumumba University,**6**(1968), 147-152.- (with J. Lewowicz and E. Lima de Sa)
*Lyapunov Functions of Two Variables and a Conjugacy Theorem for Dynamical Systems*, Acta Cientifica Venezolana**32**(6) (1981), 463-468. - (with J. Lewowicz)
*Local Conjugacy for Quasi-Hyperbolic Systems, in Differential Equations: Qualitative Theory*, Vol. 2, B. Sz-Nagy and L. Hatvani ed., North Holland, 1987, 687-704. - (with J. Lewowiz)
*On Expansive Diffeomorphisms in the Co-border of the Set of Anosov Diffeomorphisms, Proceedings of the VII ELAM*, Caracas, July 1984. - (with W. Geller)
*Maximal Entropy Orbit Types*, Transaction of the Amer. Math. Soc.**329**(1992), 161-171. - (with M. Misiurewicz)
*Entropy of Snakes and the Restricted Variational Principle*, Ergodic Theory and Dynamical Systems**12**(1992), 791-802. - (with J. Lewowicz)
*On Stable and Unstable Sets of Homeomorphisms, in Dynamical Systems,*Pitman Research Notes in Mathematics Series, 285 (1993) 117-130. - (with J. Lewowicz)
*Genericity of Homeomorphisms with Connected Stable and Unstable Sets*, Contemporary Mathematics**152**(1993), 203-213. *Learning from Disastrous Teaching Experience*, The Teaching Professor 17 (2003), no. 1, p. 4.*The Method of Lyapunov Functions of Two Variables, in Fluids and Waves. Recent Trends in Applied Analysis*. Conference Proceedings, Contemporary Mathematics**440**, American Mathematical Society (2007), 243-271. 161-171.- (with Y. Shen)
*The Weighted Fermat Triangle Problem*, International Journal of Mathematics and Mathematical Sciences**2008**(2008) ID 283846, 1-16. Doi:10.1155/2008/283846. *Geometric Methods for the Study of Local Stability*, Journal of Nonlinear Analysis, Elevier,**71**(2009) e2565-e2568.*How tan(x) grows*, note in The College Mathematics Journal 41, no. 3 (2010), 219-220.- (with J. Lewowicz and J. Groissman)
*A Survey of the Method of Lyapunov Functions of Two Variables in the Study of Stability and Persistence of Dynamical Systems*, Chapter 2 in the book Dynamical Systems. Theory, Applications, and Future Directions, J. M. Tchuenche ed., Nova Publishers, NY, 2013. - (with B. Rapatski)
*Modeling and Analysis of the San Francisco City Clinic Cohort (SFCCC) HIV-Epidemic Including Treatmant*, Mathematical Biosciences and Engineering**11**(2014) 599-619. - (with B. Rapatski)
*The San Francisco MSM epidemic: a Retrospective Analysis*, MDPI Mathematics 3 (2015), 1083-1094, http://www.mdpi.com/2227-7390/3/4/1083/pdf.

**Preprints**

- (with V. Smirnov)
*The Sharkovsky Theorem*, arXiv:1702.07964, February 2017.

**Books**

*Trigonometry*, Simon Bolivar University, Caracas, Venezuela, 1980.*Calculus 1*, Stockton University, 1998. Corrected and enlarged editions 1999, 2001, and 2004.- (with Lance Olsen and Hannah Ueno)
*The Inner Life of Art and Mathematics*, Stockton University, 2001.