in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by Ali Mohammad-Djafari, AIP Conf. Proc. 872, 243-251 (2006); arXiv: physics/0702011 (2007).

[120] C. Cafaro, Information-Geometric Indicators of Chaos in Gaussian Models on Statistical Manifolds of Negative Ricci Curvature, arXiv: nlin.CD/0702029, (2007); C. Cafaro, Information Geometry and Chaos on Negatively Curved Statistical Manifolds, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by K. Knuth et. al, AIP Conf. Proc. (2007).

[121] C. Cafaro and S. A. Ali, Jacobi Fields on Statistical Manifolds of Negative Curvature, Physica D234, 70-80 (2007); arXiv: nlin.CD/0702027 (2007).

[122] A. Caticha, Entropic Dynamics, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by R.L. Fry, AIP Conf. Proc. 617, 302 (2002).

[123] A. Caticha, Relative Entropy and Inductive Inference, Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by G. Erickson and Y. Zhai, AIP Conf. Proc. 707, 75 (2004); A. Caticha and A. Giffin, Updating Probabilities, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by Ali Mohammad-Djafari, AIP Conf. Proc. 872, 31-42 (2006); A. Caticha and R. Preuss, Maximum entropy and Bayesian data analysis: Entropic prior distributions, Phys. Rev. E70, 046127 (2004).

[124] G. Casati and B. Chirikov, Quantum Chaos, Cambridge University Press (1995).

[125] F. De Felice and J. S. Clarke, Relativity on Curved Manifolds, Cambridge University Press (1990); M. P. do Carmo, Riemannian Geometry, Birkhauser, Boston, 1992.

[126] N. S. Krylov, Works on the Foundations of Statistical Physics, Princeton University Press, Princeton, 1979.

[127] M. Pellicott, Exponential Mixing for the Geodesic Flow on Hyperbolic Three-Manifolds, Journal of Statistical Physics 67, 667 (1992).

[128] J. Jost, Compact Riemann Surfaces: An Introduction to Contemporary Mathematics, Springer-Verlag (1997).

[129] C. G. J. Jacobi, Vorlesungen uber Dynamik, Reimer, Berlin (1866).

[130] M. Biesiada, The Power of the Maupertuis-Jacobi Principle- Dreams and Reality, Chaos, Solitons & Fractals 5, 869 (1994).

[131] M. Biesiada, Searching for an invariant description of chaos in general relativity, Class. Quantum Grav. 12, 715 (1995).

[132] J. M. Lee, Riemannian Manifolds: An Introduction to Curvature, Springer Verlag (1997).

[133] M. P. do Carmo, Riemannian Geometry, Birkhauser, Boston, 1992.

[134] D. E. Hodgkinson, A modified equation of geodesic deviation, Gen. Rel. Grav. 3, 351 (1972).

[135] D. P. Feldman and J. P. Crutchfield, Measures of complexity: Why?, Phys. Lett. A238, 244-252 (1998); A. Manning, Topological entropy for geodesic flows, Annals of Mathematics 110, 567-573 (1979).

[136] S. Stenholm and K. Suominen, Quantum Approach to Informatics, Wiley-Interscience (2005).

[137] R. Schack and C. M. Caves, Hypersensitivity to perturbation: An information-theoretical characterization of classical and quantum chaos, in Quantum Communication, Computing, and Measurement, edited by O. Hirota, A. S. Holevo, and C. M. Caves, 317-330 (1997).

[138] F. Benatti, Deterministic Chaos in Infinite Quantum Systems, Springer-Verlag Berlin (1993); F. Benatti, Classical and Quantum Entropies: Dynamics and Information, in Entropy edited by A. Greven et. al., Princeton Series in Applied Mathematics (2003).

[139] R. Alicki and M. Fannes, Defining Quantum Dynamical Entropy, Lett. Math. Phys. 32, 75-82 (1994); R. Alicki and M. Fannes, Quantum Dynamical Systems, Oxford University Press (2001).

[140] A. Connes et. al., Dynamical Entropy of C ∗ Algebras and von Neumann Algebras, Commun. Math. Phys. 112, 691-719(1987).

[141] W. H. Zurek, Phys. Today 44. No 10, 36 (1991); 46, No. 12, 81 (1993); Prog. Theor. Phys. 89, 281 (1993).

[142] M. Biesiada and S. E. Rugh, Maupertuis principle, Wheeler’s superspace and an invariant criterion for local stability in general relativity, arXiv: gr-qc/9408030 (1994).

[143] J. Stewart, Advanced General Relativity, Cambridge University Press (1991).