Home Meet Arno Seminar Courses Publications Benford Online Bibliography

 

 

 

 

Textbook

  • Chaos and Chance, An Introduction to Stochastic Aspects of Dynamics, deGruyter Textbook, deGruyter, Berlin-New York, 2001.

Chaos and Chance book cover With emphasis on stochastic aspects of deterministic systems this short book introduces the reader to the basic facts and some special topics of applied ergodic theory. It adresses advanced undergraduate and graduate students from various disciplines, i.e. mathematicians, physicists, electrical and mechanical engineers. Based upon a sound (but non-technical) mathematical introduction, a number of typical examples from applications (mostly from mechanics) are thoroughly discussed. By studying both probabilistic and deterministic features of dynamical systems the reader will develop what might be considered a unified view on chaos and chance as two sides of the same thing.


Publisher's site (opens a new window or tab)



Articles

  • Large spread does not imply Benford's Law, preliminary draft (PDF, 96KB).
  •  
  • Fundamental Flaws in Feller's Classical Derivation of Benford's Law (with T. Hill), preprint (PDF, 99KB).
  •  
  • Finite-state Markov Chains Obey Benford's Law (with B. Kaynar, T. Hill, and A. Ridder), preprint (PDF, 275KB).
  •  
  • On finite-time hyperbolicity, to appear in Discrete Contin. Dyn. Syst. Ser. S.
  •  
  • Some dynamical properties of Benford sequences, to appear in J. Difference Equ. Appl.
  •  
  • A definition of spectrum for differential equations on finite time (with T.S. Doan and S. Siegmund), J. Differential Equations 246 (2009), 1098-1118.
  •  
  • Scale-distortion inequalities for mantissas of finite data sets (with T. Hill and K. Morrison), J. Theoret. Probab. 21 (2009), 97-117.
  •  
  • Nonautonomous finite-time dynamics (with T.S. Doan and S. Siegmund), Discrete Contin. Dyn. Syst. Ser. B. 9 (2008), 463-492.
  •  
  • Counting uniformly attracting solutions of nonautonomous differential equations, Discrete Contin. Dyn. Syst. Ser. S 1 (2008), 15-25.
  •  
  • Uniformly attracting solutions of nonautonomous differential equations (with S. Siegmund), Nonlinear Analysis 68 (2008), 3789-3811.
  •  
  • On the distribution of mantissae in nonautonomous difference equations (with S. Siegmund), J. Difference Equ. Appl. 13 (2007), 829-845.
  •  
  • Newton's Method obeys Benford's Law (with T. Hill), Amer. Math. Monthly 114 (2007), 588-601.
  •  
  • A Characterisation of Newton maps (with T. Hill), ANZIAM J. 48 (2006), 1-13.
  •  
  • Chaos in spatially extended systems via the Peak-Crossing Bifurcation (with L. Bunimovich), Internat. J. Bifur. Chaos Appl. Sci. Engrg. 15 (2005), 11, 1-15.
  •  
  • Benford's Law in power-like nonautonomous dynamical systems, Stoch. Dyn 5 (2005), 1-21.
  •  
  • One-dimensional dynamical systems and Benford's law (with L. Bunimovich and T. Hill), Trans. Amer. Math. Soc. 357 (2005), 197-219.
  •  
  • Multi-dimensional dynamical systems and Benford's law, Discrete Contin. Dyn. Syst. Ser. A 13 (2005), 219-237.
  •  
  • Almost automorphic dynamics in symbolic lattices (with S. Siegmund and Y. Yi), Ergodic Theory Dyn. Syst. 24 (2004), 677-696.
  •  
  • A criterion for non-persistence of travelling breathers for perturbations of the Ablowitz-Ladik lattice (with R.S. MacKay and V.M. Rothos), Discrete Contin. Dyn. Syst. Ser. B 4 (2004), 911-920.
  •  
  • On the gap between random dynamical systems and continuous skew products, (with S. Siegmund), J. Dynam. Differential Equations 15 (2003), 237-279.
  •  
  • On the appropriate treatment of singularly perturbed wave equations (with M. Schagerl), Z. Angew. Math. Mech. 81 (2001), 623-624.
  •  
  • Propagation of small waves in inextensible strings (with M. Schagerl), Wave Motion 35 (2001), 339-353.
  •  
  • On the regular and chaotic motion of a kicked pendulum: a Markovian approach, Z. Angew. Math. Mech. 81 (2001), 611-612.
  •  
  • Zur Stabilität eines Doppelpendels mit geradlinig geführtem Endpunkt, Z. Angew. Math. Mech. 80 (2000), 335-336.
  •  
  • Rigorous error bounds for RK methods in the proof of chaotic behaviour, J. Comput. Appl. Math. 111 (1999), 13-24.
  •  
  • Zum praktischen Nachweis von Chaos mit Hilfe der Conley Index Theorie, Z. Angew. Math. Mech. 79 (1999), 791-792.

Other publications

  • RK methods and the proof of chaotic behaviour, Proc. of the Second Meeting on Numerical Methods for Differential Equations, Coimbra, 1998.
  •  
  • Dynamics and Digits: On the Ubiquity of Benford's Law, Proceedings of Equadiff 2003, World Scientific, Singapore, 2005, 693-695.
  •  
  • Two Notions of Finite-Time Hyperbolicity (with T.S. Doan and S. Siegmund), to appear in Proceedings of Equadiff 2007.
  •  
  • More on finite-time hyperbolicity, to appear in Bol. Soc. Esp. Mat. Apl.
  •  

Book reviews

  • M. Denker: Einführung in die Analysis dynamischer Systeme, Book review, Z. Angew. Math. Mech. 86 (2006), 251-252.
  •  
  • T. Kaczynski, M. Mischaikow, M. Mrozek: Computational Homology, Book review, Z. Angew. Math. Mech. 86 (2006), 334-335.
  •  
  • G. H. Choe: Computational Ergodic Theory, Book review, Z. Angew. Math. Mech. 86 (2006), 743-744.
  •  
  • R. Taschner: The Continuum, Book review, to appear in Z. Angew. Math. Mech., 2007.