Dynamical systems and their applications

Programa: 
First Session: Introduction to dynamical systems [1,2,3] 
Jueves 23 de noviembre de 2017, 11:30-14:00, Seminario 1ª planta IEMath-GR

• What is a dynamical system (DS)? Discrete and continuous time.
• The orbit of a DS.
• One dimensional DS, hyperbolic points.
• On a family of quadratic DSs.

Second Session: Applications to biology [4-7] 
Martes 28 de noviembre de 2017, 11:30-14:00, Seminario 2ª planta IEMath-GR

• Definitions of QSO.
• The Volterra QSOs.
• Examples of Non-Volterra QSOs.

Third Session: Thermodynamics in physics [8-10] 
Jueves 30 de noviembre de 2017, 11:30-14:00, Sala de Conferencias IEMath-GR

• Gibbs measure.
• Configuration space. Hamiltonian.
• A functional equation for the Ising model.
• Periodic Gibbs measures of the Ising model.

References.

1. R.L. Devaney. An introduction to Chaotic dynamical systems. Westview press. 2003.
2. R.C.Robinson. An introduction to dynamical systems, continuous and discrete. Pearson Educ.Inc. 2004.
3. S.N.Elaydi. Discrete chaos. Chapman Hall/CRC. 2000
4. Ганиходжаев Р.Н. Квадратичные стохастические операторы. Доктор.Дисс. 1992.
5. Ganikhodzhaev R.N., Mukhamedov F.M., Rozikov U.A. Quadratic stochastic operators and processes: results and open problems. Inf. Dim. Anal. Quant. Prob. Rel. Fields. 2011. V.14, No.2, p.279-335.
6. R. N. Ganikhodzhaev, Quadratic stochastic operators, Lyapunov functions and tournaments, Acad. Sci. Sb. Math. 76 (1993) 489–506.
7. R. N. Ganikhodzhaev, A chart of fixed points and Lyapunov functions for a class of discrete dynamical systems, Math. Notes 56 (1994) 1125–1131
8. Rozikov U.A. Gibbs measures on Cayley trees. World Sci. Publ. Singapore. 2013, 404 pp.
9. Ya.G. Sinai, Theory of phase transitions: Rigorous Results, Pergamon, Oxford, 1982.
10. H.O. Georgii, Gibbs Measures and Phase Transitions, Second edition. De Gruyter Studies in Mathematics, 9. Walter de Gruyter, Berlin, 2011