G. Keller,
Equilibrium States in Ergodic Theory
pp. 185, Cambridge University Press (1998).

A. Greven, G. Keller, G. Warnecke (Eds.)
, (table of contents)
pp. 358, Princeton Series in Applied Mathematics, Princeton University Press (2003)

G. Keller,
Mathematik in den Life Sciences
pp. 232, UTB Ulmer (2011)

A supervised M.S. Thesis:

J. Seifert,
On the ergodic theory of B-free dynamics (2017)

Publications in Journals and Proceedings

91. S. Fadaei, G. Keller, F.H. Ghane
Invariant graphs for chaotically driven maps. Nonlinearity 31 (2018), 5329–5349. Preprint arxiv:1804.08370

90. G. Keller
Tautness of sets of multiples and applications to B-free dynamics (2018) arxiv:1802.08309 To appear in Studia Mathematica.

89. P. Bálint, G. Keller, F.M. Sélley, I.P. Tóth
Stability of the invariant distribution for a class of globally coupled maps. Preprint (2017) arXiv:1711.05461. Nonlinearity 31 (2018), 3770–3793,

88. G. Keller
Generalized heredity in B-free systems. Preprint (2017) arXiv:1704.04079

87. G. Keller, C. Richard
Periods and factors of weak model sets. Israel J. Math. online first DOI 10.1007/s11856-018-1788-8, Preprint (2017) arXiv:1702.02383

86. S. Kasjan, G. Keller, M. Lemanczyk
Dynamics of B-free sets: A view through the window, International Mathematics Research Notices, Vol. 2019, Issue 9, Pages 2690-2734,

85. G. Keller, A. Otani
Chaotically driven sigmoidal maps.
Stochastics & Dynamics 18 (2) (2017). Online Ready

84. G. Keller
Maximal equicontinuous generic factors and weak model sets. Preprint (2016) arXiv:1610.03998.

83. G. Keller, C. Richard
Dynamics on the graph of the torus parametrisation. Preprint (2015) arXiv:1511.06137. Ergod. Th. & Dynam. Sys. (online)

82. G. Keller
Stability index, uncertainty exponent, and thermodynamic formalism for intermingled basins of chaotic attractors. Discrete and Continuous Dynamical Systems – Series S 10 (2017), 313-334. doi:10.3934/dcdss.2017015

81. G. Keller
An elementary proof for the dimension of the graph of the classical Weierstrass function. Annales de l’Institut Henri Poincaré – Probabilités et Statistiques 53 (2017), 169-181. File

80. V. Anagnostopoulou, T. Jäger, G. Keller
A model for the nonautonomous Hopf bifurcation, Nonlinearity 28 (2015), 2587-2616.

79. G. Keller, H. Jafri, R. Ramaswamy
The nature of weak generalized synchronization in chaotically driven maps, Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Apr;87(4):042913

78. T. Jäger, G. Keller
Random minimality and continuity of invariant graphs in random dynamical systems, arXiv:1211.5885, Transactions Amer. Math. Soc. 368 (2016) ,6643–6662.

77. G. Keller
Stability index for chaotically driven concave maps, Journal of the London Mathematical Society 89 (2014), 603-622;
doi: 10.1112/jlms/jdt070

76. G. Keller, A. Otani
Bifurcation and Hausdorff dimension in families of chaotically driven maps with multiplicative forcing
Dynamical Systems: An International Journal 28 (2013), 123-139. ePrint

75. G. Keller
Rare events, exponential hitting times and extremal indices via spectral perturbation, Dynamical Systems: An International Journal 27 (2012), 11-27. Reprint

74. J.-B. Bardet, G. Keller, R. Zweimüller
Stochastically stable globally coupled maps with bistable thermodynamic limit,
Communications in Mathematical Physics 292 (2009), 237-270,  Preprint (2008)

73. G. Keller, C. Liverani
Map lattices coupled by collisions,
Communications in Mathematical Physics 291 (2009), 591-597, DOI:10.1007/s00220-009-0835-z,  Preprint (2008)

72. G. Keller, C. Liverani
Rare events, escape rates and quasistationarity: some exact formulae, Journal of Statistical Physics 135 (2009), 519-534, Preprint (2008).

71. P. Howard, G. Keller, R. Klages
Continuity properties of transport coefficients in simple maps,Nonlinearity 21(2008), 1719-1743.

70. D. Dolgopyat, G. Keller, C. Liverani
Random walk in Markovian environment, Annals of Probability 36 (2008), 1676-1710. Preprint.

69. J.-B. Bardet, S. Gouëzel, G. Keller
Limit theorems for coupled interval maps, Stochastics and Dynamics 7 (2007), 17-36. Preprint (2006)

68. H. Fujisaki, G. Keller
The central limit theorem for the normalized sums of the MAI for SSMA communication systems using spreading sequences of Markov chains,
IEICE Transactions of Fundamentals of Electronics, Communications and computer Sciences E89-A (2006), 2307-2314.

67. Jean-Baptiste Bardet, G. Keller
Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling, Nonlinearity 19 (2006), 2193-2210. (Here is an
erratum that fills two gaps in the proofs. The results are unchanged.)

66. P. Glendinning, T. Jäger, G. Keller
How chaotic are strange nonchaotic attractors? Nonlinearity 19 (2006), 2005-2022.

65. G. Keller, C. Liverani
Uniqueness of the SRB measure for piecewise expanding weakly coupled map lattices in any dimension, Commun. Math. Phys. 262 (2006), 33-50. Preprint

64. T. Jäger, G. Keller
The Denjoy type-of argument for quasiperiodically forced circle diffeomorphisms, Ergod. Th. &Dynam. Sys. 26 (2006), 447-465.  Preprint

63. R. Fabbri, T. Jäger, R. Johnson, G. Keller
A Sharkovskii-type theorem for minimally forced interval maps, Topological Methods in Nonlinear Analysis 26 (2005), 163-188. Preprint

62. G. Keller, C. Liverani
A spectral gap for a one-dimensional lattice of coupled piecewise expanding interval maps, in: Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems (Eds.: J.-R. Chazottes, B. Fernandez), Lecture Notes in Physics 671 (2005), pp. 115-151, Springer Verlag. Preprint

61. G. Keller, C. Liverani
Coupled map lattices without cluster expansion, Discr. Cont. Dynam. Sys. 11 (2004), 325-335.Preprint

60. G. Keller, H.H. Rugh
Eigenfunctions for smooth expanding circle maps, Nonlinearity 17 (2004), 1723-1730. Preprint

59. S. Datta, T. Jäger, G. Keller, R. Ramaswamy
On the dynamics of the critical Harper map, Nonlinearity 17 (2004), 2315-2323. Preprint

58. Ch. Bandt, G. Keller, B. Pompe
Entropy of interval maps via permutations, Nonlinearity 15 (2002), 1595-1602.

57. M. Blank, G. Keller, C. Liverani
Ruelle-Perron-Frobenius spectrum for Anosov maps, Nonlinearity 15 (2002), 1905-1973.  Preprint (2001).

56. G. Keller
Completely mixing maps without limit measure, Preprint (2000), Colloq. Math. 100 (2004), 73-76.

55. G. Keller, R. Zweimüller
Unidirectionally coupled interval maps: between dynamics and statistical mechanics, Nonlinearity 15 (2002), 1-24.

54. G. Keller, M. St.Pierre
Topological and measurable dynamics of Lorenz maps, Research Report (2000). In: B. Fiedler (Ed.), Ergodic Theory, Analysis, and Efficient simulation of Dynamical Systems, Springer Verlag, 2001.

53. J. Buzzi, G. Keller
Zeta functions and transfer operators for multidimensional piecewise affine and expanding maps, Ergod. Th. &Dynam. Sys. 21 (2001), 690-716.

52. G. Keller
A note on dynamical zeta functions for S-unimodal maps, Colloquium Mathematicum 84/85 (2000), 229-233.

51. G. Keller
An ergodic theoretic approach to mean field coupled maps, Progress in Probability, Vol. 46 (2000), 183-208.

50. G. Keller, C. Liverani
Stability of the spectrum for transfer operators, Ann. Mat. Sc. Norm. Pisa 28 (1999), 141-152.

49. M. Blank, G. Keller
Random perturbations of chaotic dynamical systems: Stability of the spectrum, Nonlinearity 11 (1998), 1351-1364.

48. G. Keller
Interval maps with strictly contracting Perron-Frobenius operators, Int. J. Bifurc. Chaos 9 (1999), 1777-1784.

47. G. Keller
Mixing for finite systems of coupled tent maps, Proc. Steklov Inst. Math. 216 (1997), 315-321. (Also: Erwin-Schrödinger-Institut Preprint

46. H. Bruin, G. Keller
Equilibrium states for S-unimodal maps, Ergod. Th.&Dynam. Sys. 18 (1998), 765-789.

45. G. Keller
A new estimator for information dimension with standard errors and confidence intervals, Stoch. Proc. Appl. 71 (1997), 187-206.

44. M. Blank, G. Keller
Stochastic stability versus localization in chaotic dynamical systems, Nonlinearity 10 (1997), 81-107

43. G. Keller
A note on strange nonchaotic attractors, Fundamenta Math. 151 (1996), 139-148.

42. H. Bruin, G. Keller, M. St. Pierre
Adding machines and wild atractors, Ergod. Th.&Dynam. Sys. 17 (1997), 1267-1287.

41. M. Frank, G. Keller, R. Sporer
Practical implementation of error estimation for the correlation dimension, Phys. Review E 53(6) (1996), 5831-5836.

40. G. Keller, R. Sporer
Remarks on the linear regression approach to dimension estimation, Stochastic and spatial structures of dynamical systems (Ed.: S.J. van Strien, S.M. Verduyn Lunel) Kon. Nederl. Akad. Wetensch. Verhandelingen, Afd. Natuurkunde, Eerste Reeks, Vol. 45 (1996), 17-28. (Also available as Preprint )

39. G. Keller
Coupled map lattices via transfer operators on functions of bounded variation, Stochastic and spatial structures of dynamical systems (Ed.: S.J. van Strien, S.M. Verduyn Lunel) Kon. Nederl. Akad. Wetensch. Verhandelingen, Afd. Natuurkunde, Eerste Reeks, Vol. 45 (1996), 71-80. (Also available as Preprint)

38. H. Bruin, G. Keller, T. Nowicki, S. van Strien
Wild Cantor attractors exist, Ann. Math. 143 (1996), 97-130.

37. F. Hofbauer, G. Keller
Quadratic maps with maximal oscillation, in: Algorithms, Fractals and Dynamics, Proceedings of the Hyashibara Forum 1992, Okayama, and of a Symposium held in Kyoto 1992 (Ed.: Y. Takahashi), Plenum Publ. (1995).

36. F. Hofbauer, G. Keller
Equilibrium states and Hausdorff measures for interval maps, Mathem. Nachrichten 164 (1993), 239-257.

35. G. Keller, T. Nowicki
Fibonacci maps re(al)visited, Ergod. Th.&Dynam. Sys. 15 (1995), 99-120.

34. G. Keller Exponential weak Bernoulli mixing for Collet-Eckmann maps, Israel J. Math. 86 (1994), 301-310.

33. R. Burton, G. Keller
Stationary measures for randomly chosen maps, J. Theor. Prob. 6 (1993), 1-16.

32. G. Keller, T. Nowicki
Spectral theory, zeta functions and the distribution of periodic orbits for Collet-Eckmann maps, Commun. Math. Phys. 149 (1992), 31-69.

31. G. Keller, M. Künzle, T. Nowicki
Some phase transitions in coupled map lattices, Physica D 59 (1992), 39-51.

30. G. Keller, M. Künzle
Transfer operators for coupled map lattices, Ergod. Th. &Dynam. Sys. 12 (1992), 297-318.

29. G. Keller
Lyapunov exponents and complexity for interval maps, in „Lyapunov Exponents“, edited by L. Arnold et al. Springer Lecture Notes in Mathematics 1486 (1991).

28. G. Keller
Circular codes, loop counting, and zeta-functions, J. Comb. Th., Series A, 56 (1991), 75-83.

27. G. Keller
On the clustering conjecture for Bernoulli factors of Bernoulli shifts, Proc. Amer. Math. Soc. 111 (1991), 51-53.

26. F. Hofbauer, G. Keller
Some remarks about recent results on S-unimodal maps, Annales de l’Institut Henri Poincaré, Physique Théorique 53 (1990), 413-425.

25. F. Hofbauer, G. Keller
Quadratic maps without asymptotic measure, Commun. Math. Phys. 127 (1990), 319-337.

24. M. Denker, G. Keller, M. Urbanski
On the uniqueness of equilibrium states for piecewise monotone mappings, Studia Math. 97 (1990), 27-36.

23. V. Baladi, G. Keller
Zeta-functions and transfer operators for piecewise monotone transformations, Commun. Math. Phys.127 (1990), 459-478.

22. G. Keller
Periodic orbits for interval maps, in „Stochastic Modelling in Biology“ edited by P. Tautu, pp. 412-419. World Scientific, Singapore (1990).

21. G. Keller
Exponents, attractors, and Hopf decompositions for interval maps, Ergod. Th. &Dynam. Sys. 10 (1990), 717-744.

20. G. Keller
Lifting measures to Markov extensions, Monatsh. Math. 108 (1989), 183-200.

19. G. Keller
Markov extensions, zeta-functions, and Fredholm theory for piecewise invertible dynamical systems, Trans. Amer. Math. Soc. 314 (1989), 433-497.

18. J.L. van Hemmen, G. Keller, R. Kühn
Forgetful memories, Europhysics Letters 5 (1988), 663-668.

17. G. Keller, G. Kersting, U. Rösler
On the asymptotic behaviour of first passage times for diffusions, Prob. Th. Rel. Fields 77 (1988), 379-395.

16. G. Keller, G. Kersting, U. Rösler
On the asymptotic behaviour of time-discrete stochastic growth processes, Annals Prob. 15 (1987), 305-343.

15. M. Denker, G. Keller, M.L. Puri
Linear rank statistics, bounded operators and weak convergence, New Perspectives in Theoretical and Applied Statistics, Wiley Publ. (1986), 171-206.

14. M. Denker, G. Keller
Rigorous statistical procedures for data from dynamical systems, J. Stat. Phys. 44 (1986), 67-93.

13. M. Denker, Ch. Grillenberger, G. Keller
A note on invariance principles and v.Mises‘ statistics, Metrika 32 (1985), 197-214.

12. G. Keller
Generalized bounded variation and applications to piecewise monotonic transformations, Z. Wahrscheinlichkeitstheorie verw. Geb. 69 (1985), 461-478.

11. G. Keller, G. Kersting und U. Rösler
On the asymptotic behaviour of solutions of stochastic differential equations, Z. Wahrscheinlichkeitstheorie verw. Geb. 68 (1984), 163-189.

10. F. Hofbauer, G. Keller
Zeta-functions and transfer-operators for piecewise linear transformations, J. reine und angew. Math. 352 (1984), 100-113.

9. G. Keller
On the rate of convergence to equilibrium in one-dimensional systems, Commun. Math. Phys. 96 (1984), 181-193.

8. M. Denker, G. Keller
On U-statistics and v.Mises‘ statistics for weakly dependent processes, Z. Wahrscheinlichkeitstheorie verw. Geb. 64 (1983), 505-522.

7. F. Hofbauer, G. Keller
Equilibrium states for piecewise monotonic transformations, Ergod. Th. &Dynam. Sys. 2 (1982), 23-43.

6. F. Hofbauer, G. Keller
Ergodic properties of invariant measures for piecewise monotonic transformations, Math. Zeitschrift 180 (1982), 119-140.

5. G. Keller
Stochastic perturbations of some strange attractors, Dynamical Systems and Chaos. Proceedings, Sitges, 1982, pp. 192-193.

4. G. Keller
Stochastic stability of some one-dimensional systems, Ergodic Theory and Related Topics. Proceedings of the Conference held in Vitte/Hiddensee 1981, pp. 123-127.

3. G. Keller
Stochastic stability in some chaotic dynamical systems, Monatshefte Math. 94 (1982), 313-333.

2. G. Keller
Un théorème de la limite centrale pour une classe de transformations monotones par morceaux, C. R. Acad. Sci. Paris, Série A, 291
(1980), 155-158.

1. G. Keller
Ergodicité et mesures invariantes pour les transformations dilatantes par morceaux d’une région bornée du plan, C. R. Acad. Sci. Paris, Série A,
289 (1979), 625-627 (Summary of my Thèse de 3me cycle).


1. G. Keller, Mathematische Statistik, Vorlesungsskript, pp. 93, (1992).
2. G. Keller, The Transfer operator approach to interval maps (1992).
3. G. Keller, Wahrscheinlichkeitstheorie I und II, Vorlesungsskript, pp. 196, (2002 -). (pdf)
4. G. Keller, Mathematik für Naturwissenschaftler (Biologen), pp. 135 (2007) (pdf)

Friedrich-Alexander-Universität Erlangen-Nürnberg