Publications

13. Complex Dynamics: Twenty Five Years After the Appearance of the Mandelbrot Set. (Coedited with L. Keen). American Mathematical Society, Contemporary Math 396, 2006.

12. Differential Equations, Dynamical Systems, and an Introduction to Chaos. Second Edition. With M. W. Hirsch and S. Smale. Elsevier Academic Press, 2004.

11. The Mandelbrot and Julia Sets. Key Curriculum Press, 2000.

10. Chaos. With J. Choate. Key Curriculum Press, 2000.

9. Fractals. With J. Choate and A. Foster. Key Curriculum Press, 1999.

8. Iteration. With J. Choate and A. Foster. Key Curriculum Press, 1999.

7. Differential Equations. With P. Blanchard and G. R. Hall. First Edition. Brooks/Cole, 1998. Spanish Translation: Ecuaciones Diferenciales. International Thomson Editores. Mexico, 1999. Second Edition. Brooks/Cole, 2002. Third Edition, 2005.

6. Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets. Editor. American Mathematics Society, 1994.

5. A First Course in Chaotic Dynamical Systems: Theory and Experiment. Perseus Press, 1992. French Translation: Editions Addison-Wesley France, Paris. Japanese Translation, 1997, by Addison-Wesley.

4. Chaos and Fractals: The Mathematics Behind the Computer Graphics. Coedited with L. Keen. American Mathematics Society, 1989.

3. Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics. Menlo Park, Calif.: Addison-Wesley, 1989. Italian Translation: Caos e Frattali---Matematica dei Sistemi Dinamici e Applicazioni al Calcolatore. Libreria Ulrico Hoepli, Milano, 1990. Dutch Translation: Chaos, Fractals, Dynamica: Computer-Experimenten in de Wiskunde. Addison-Wesley: Amsterdam.

2. An Introduction to Chaotic Dynamical Systems. Redwood City, Calif.: Addison-Wesley, 1986. Second Edition, 1989. Japanese Translation by Kyoritsu Press, 1988. Second Edition, 1990.

1. Classical Mechanics and Dynamical Systems. Coedited with Z. Nitecki. New York: Marcel Dekker, Inc., 1981.

100. Dynamic Classification of Escape Time Sierpinski Curve Julia Sets (with K. Pilgrim). To appear.

99. A Generalized Version of the McMullen Domain (with P. Blanchard, A. Garijo, and E. Russell). To appear in International Journal of Bifurcation and Chaos.

98. Limiting Julia Sets for Singularly Perturbed Rational Maps (with M. Morabito). To appear in International Journal of Bifurcation and Chaos.

97. Rabbits, Basilicas, and Other Julia Sets Wrapped in Sierpinski Carpets (with P. Blanchard, A. Garijo, S. Marotta, and E. Russell). To appear.

96. Singular Perturbations in the McMullen Domain (with S. Marotta). To appear.

95. Julia Sets Converging to the Unit Disk (with A. Garijo). To appear in Proceedings of the American Mathematical Society.

94. Complex Exponential Dynamics. To appear.

93. Cantor Sets of Circles of Sierpinski Curve Julia Sets. Ergodic Theory and Dynamical Systems 27 (2007), 1525-1539.

92. Evolution of the McMullen Domain for Singularly Perturbed Rational Maps (with S. Marotta). To appear in Topology Proceedings.

91. Cantor Webs in the Parameter and Dynamical Planes of Rational Maps. Fields Institute Communications 53 (2008).

90. Open Problems in Complex Dynamics and "Complex" Topology. In Open Problems in Topology II, ed. Elliott Pearl, Elsevier (2007), 469-478.

89. A Myriad of Sierpinski Curve Julia Sets. In Difference Equations, Special Functions and Orthogonal Polynomials. World Scientific (2007), 131-148.

88. The McMullen Domain: Satellite Mandelbrot Sets and Sierpinski Holes. Conformal Geometry and Dynamics 11 (2007), 164-190.

87. Cantor Necklaces and Structurally Unstable Sierpinski Curve Julia Sets for Rational Maps. Qualitative Theory of Dynamical Systems 5 (2006), 337-359.

86. The McMullen Domain: Rings Around the Boundary (with S. Marotta). Transactions of the American Mathematical Society 359 (2007), 3251-3273.

85. Singular Perturbations of zⁿ (with M. Holzer, D. M. Look, M. Moreno Rocha, and D. Uminsky). To appear in Transcendental Dynamics and Complex Analysis, eds. P. Rippon and G. Stallard. Cambridge University Press.

84. Rational Maps with Generalized Sierpinski Gasket Julia Sets (with M. Moreno Rocha and S. Siegmund). Topology and its Applications 154 (2007), 11-27.

83. A Criterion for Sierpinski Curve Julia Sets. (with D. M. Look). Topology Proceedings 30 (2006), 163-179.

82. Sierpinski Carpets and Gaskets As Julia Sets of Rational Maps. (with P. Blanchard, D. M. Look, M. Moreno Rocha, P. Seal, S. Siegmund, and D. Uminsky). In Dynamics on the Riemann Sphere, eds. P. Horth and C. Petersen. European Math Society (2006), 97-119.

81. Baby Mandelbrot Sets Adorned with Halos in Families of Rational Maps. In Complex Dynamics: Twenty-Five Years After the Appearance of the Mandelbrot Set, American Mathematical Society. Contemporary Math 396 (2006), 37-50.

80. Blowup Points and Baby Mandelbrot Sets for Singularly Perturbed Rational Maps. (with M. Holzer and D. Uminsky). In Complex Dynamics: Twenty-Five Years After the Appearance of the Mandelbrot Set. American Mathematical Society. Contemporary Math 396 (2006), 51-62.

79. Indecomposable Continua and Misiurewicz Points in Exponential Dynamics (with X. Jarque and M. Moreno Rocha). International Journal of Bifurcation and Chaos 15 (2005), 3281-3293.

78. Buried Sierpinski Curve Julia Sets. (with D. M. Look). Discrete and Continuous Dynamical Systems 13 (2005), 1035-1046.

77. Sierpinski Curve Julia Sets and Singular Perturbations of Complex Polynomials. (with P. Blanchard, D. M. Look, P. Seal, Y. Shapiro). Ergodic Theory and Dynamical Systems 25 (2005), 1047-1055.

76. Structure of the McMullen Domain in the Parameter Planes for Rational Maps. Fundamenta Mathematicae 185 (2005), 267-285.

75. The Escape Trichotomy for Singularly Perturbed Rational Maps. (with D. M. Look and D. Uminsky). Indiana University Mathematics Journal 54 (2005), 1621-1634.

74. Symbolic Dynamics for a Sierpinski Curve Julia Set (with D. M. Look). Journal of Difference Equations and Applications 11 (2005), 581-596.

73. Topological Bifurcations. Topology Proceedings 28 (2004), 99-112.

72. Playing Catchup with Iterated Exponentials (with K. Josic, M. Moreno Rocha, P. Seal, Y. Shapiro, A. T. Frumosu). The American Mathematical Monthly 111 (2004), 704-708.

71. Singular Perturbations of Quadratic Maps (with K. Josic and Y. Shapiro). International Journal of Bifurcations and Chaos 14 (2004), 161-169.

70. Complex Dynamics and Symbolic Dynamics (with P. Blanchard and L. Keen). In Symbolic Dynamics and its Applications. Proceedings of the Symposia in Applied Math 60 (2004), 37-60.

69. A Survey of Exponential Dynamics. In: New Progress in Difference Equations, eds. B. Aulbach, S. Elaydi, and G. Ladas. Chapman & Hall/CRC (2004), 105-122.

68. Cantor and Sierpinski, Julia and Fatou: Complex Topology Meets Complex Dynamics. Notices of the American Mathematical Society 51 (2004), 9-15.

67. A Semilinear Model for Exponential Dynamics and Topology (with M. Moreno Rocha). Topology Proceedings 26 (2002), 153-167.

66. Indecomposable Continua in Exponential Dynamics (with X. Jarque). Conformal Geometry and Dynamics 6 (2002), 1-12.

65. The Fractal Geometry of the Mandelbrot Set: I. Periods of the Bulbs. In Fractals, Graphics, and Mathematics Education. MAA Notes 58 (2002), 61-68.

64. Hyperbolic Components of the Complex Exponential Family (with N. Fagella and X. Jarque). Fundamenta Mathematicae. 174 (2002), 193-215.

63. Geometry of the Antennas in the Mandelbrot Set (with M. Moreno Rocha). Fractals. 10 (2002), 39-46.

62. Accessible Points in the Julia Sets of Stable Exponentials (with R. Bhattacharjee, R. E. Lee Deville, K. Josic, M. Moreno Rocha). Discrete and Continuous Dynamical Systems. 1 (2001), 299-318.

61. Homoclinic Points in Complex Dynamical Systems. In Global Analysis of Dynamical Systems, eds. H. Broer, B. Krauskopf, G. Vegter. IOP Publishing (2001), 329-338.

60. Se^x: Dynamics, Topology, and Bifurcations of Complex Exponentials. Topology and its Applications 110 (2001), 133-161.

59. Tying Hairs for Structurally Stable Exponentials (with R. Bhattacharjee). Ergodic Theory and Dynamical Systems 20 (2000), 1603-1617.

58. Dynamical Convergence of Polynomials to the Exponential (with C. Bodelon, M. Hayes, L. Goldberg, J. Hubbard and G. Roberts). Journal of Difference Equations and Applications 6 (2000), 275-307.

57. Baby Mandelbrot Sets are Born in Cauliflowers (with X. Buff, A. Douady and P. Sentenac). In The Mandelbrot Set: Theme and Variations, London Mathematical Society Lecture Notes, Cambridge University Press, ed. Tan Lei. 274 (2000), 19-36.

56. Hairs for the Complex Exponential Family (with C. Bodelon, M. Hayes, L. Goldberg, J. Hubbard and G. Roberts). Bifurcation and Chaos 9 (1999), 1517-1534.

55. Cantor Bouquets, Explosions, and Knaster Continua: Dynamics of Complex Exponentials. Publicacions Matematiques 43 (1999), 27-54.

54. The Mandelbrot Set, the Farey Tree, and the Fibonacci Sequence. American Mathematical Monthly 106 (1999), 289-302.

53. Caos. Enciclopedia del Novecento. Istituto della Enciclopedia Italiana. 10 (1998), 176-187.

52. Misiurewicz Points for Complex Exponentials (with X. Jarque). International Journal of Bifurcation and Chaos 7 (1997), 1599-1616.

51. The Dynamics of a Piecewise Linear Map and Its Smooth Approximation (with D. Aharonov and U. Elias). International Journal of Bifurcation and Chaos 7 (1997), 351-372.

50. The Fractal Geometry of the Mandelbrot Set: II. How to Add and How to Count. Fractals 3 No. 4 (1995), 629-640.

49. The Complex Dynamics of Quadratic Polynomials. Proceedings of the Symposia in Applied Mathematics. 49, (1995), 1-27.

48. Complex Dynamics and Entire Functions. Proceedings of the Symposia in Applied Mathematics. 49 (1995), 181-206.

47. Open Questions in Non-rational Complex Dynamics. In Problems in Holomorphic Dynamics. Springer-Verlag Lecture Notes in Mathematics 1574 (1994).

46. Chaotic Dynamics and Julia Sets. In Fractals in Nature and in Mathematics Enciclopedia Italiana (1993), 51-60.

45. Knaster-like Continua and Complex Dynamics. Ergodic Theory and Dynamical Systems 13 (1993), 627-634.

44. Chaotic Bursts in Complex Dynamical Systems. In Applications of Fractals and Chaos. Springer-Verlag, (1993), 195-206.

43. The Gingerbreadman. Algorithm 3 (1992), 15-16.

42. e^z: Dynamics and Bifurcations. Bifurcations and Chaos. 1 (1991), 287-308.

41. The Dynamics of Complex Polynomials and Automorphisms of the Shift (with P. Blanchard and L. Keen). Inventiones Mathematicae 104 (1991), 545-580.

40. The Exploding Exponential and Other Chaotic Bursts in Complex Dynamics (with M. Durkin.) American Mathematical Monthly 98 (1991), 217-233.

39. The Orbit Diagram and the Mandelbrot Set. The College Mathematics Journal 22 (1991), 23-38.

38. Chaotic Explosions in Simple Dynamical Systems. In The Ubiquity of Chaos, ed. S. Krasner, AAAS (1990), 1-9.

37. Dynamics of Entire Maps. In Workshop on Dynamical Systems, International Center for Theoretical Physics, Trieste, 1988. Longman Scientific: Pitman Research Notes in Mathematics. 221 (1990), 1-10.

36. Dynamics of Simple Maps. In Chaos and Fractals: The Mathematics Behind the Computer Graphics, American Mathematical Society, (1989), 1-24.

35. Dynamics of Entire Maps. Dynamical Systems and Ergodic Theory. Banach Center Publications 23 (1989), 221-228.

34. Dynamics of Meromorphic Maps: Maps with Polynomial Schwarzian Derivative (with L. Keen.) Annales Scientifiques de l'Ecole Normale Superieure 22 (1989), 55-79.

33. Dynamics of Tangent (with L. Keen.) In Dynamical Systems, Proceedings, University of Maryland, Springer-Verlag Lecture Notes in Mathematics. 1342 (1988), 105-111.

32. Reversibility, Homoclinic Points, and the Henon Map. In Dynamical Systems Approaches to Nonlinear Problems in Systems and Circuits. Philadelphia: SIAM, (1988), 3-14.

31. Dynamics of Maps with Constant Schwarzian Derivative (with L. Keen.) In Proceedings of the Nevanlinna Colloquium. Springer-Verlag Lecture Notes 1351 (1987).

30. Chaotic Bursts in Nonlinear Dynamical Systems. Science. 235 (1987), 342-345.

29. Uniformization of Attracting Basins for Exponential Maps (with L. Goldberg.) Duke Mathematics Journal 55 (1987), 253-266.

28. Dynamics near an Essential Singularity (with F. Tangerman.) Ergodic Theory and Dynamical Systems 6 (1986), 489-503.

27. Exploding Julia Sets. In Chaotic Dynamics and Fractals. New York: Academic Press, Inc. (1986), 141-154.

26. Symbolic Dynamics of Complex Exponential Maps. In Proceedings of the 1983 Beijing Symposium on Differential Geometry and Differential Equations. Science Press, Beijing, China (1986), 329-334.

25. Structural Instability of Exp(z). Proceedings of the American Mathematical Society 94 (1985), 545-548.

24. Dynamics of Exp(z) (with M. Krych.) Ergodic Theory and Dynamical Systems 4 (1984), 35-52.

23. Bursts into Chaos. Physics Letters 104 (1984), 385-387.

22. Julia Sets and Bifurcation Diagrams for Exponential Maps. Bulletin of the American Mathematical Society 11 (1984), 167-172.

21. A Piecewise Linear Model for the Zones of Instability of an Area Preserving Map. Physica D 10 (1984), 387-393.

20. Homoclinic Bifurcations and the Area-conserving Henon Map. Journal of Differential Equations 51 (1984), 254-266.

19. Blowing Up Singularities in Classical Mechanical Systems. American Mathematical Monthly 89 (1982), 535-552.

18. Motion Near Total Collapse in the Planar Isosceles Three Body Problem. Celestial Mechanics 28 (1982), 25-36.

17. Three Area-Preserving Mappings Exhibiting Stochastic Behavior. In: Classical Mechanics and Dynamical Systems. New York: Marcel Dekker, Inc. (1981), 39-53.

16. The Baker Transformation and a Mapping Associated to the Restricted Three Body Problem. Communications in Mathematical Physics 80 (1981), 465-476.

15. Genealogy of Periodic Points of Maps of the Interval. Transactions of the American Mathematical Society 265 (1981), 136-146.

14. Linked Twist Mappings Are Almost Anosov. In Global Theory of Dynamical Systems. New York: Springer-Verlag, (1980), 121-145.

13. Morse-Smale Singularities in Simple Mechanical Systems. Journal of Differential Geometry 15 (1980), 285-305.

12. Triple Collision in the Planar Isosceles Three Body Problem. Inventiones Mathematicae 60 (1980), 249-267.

11. Shift Automorphisms in the Henon Mapping (with Z. Nitecki.) Communications in Mathematical Physics 67 (1979), 137-146.

10. Structural Stability of Homothetic Solutions of the Collinear N-Body Problem. Celestial Mechanics 19 (1979), 108-117.

9. Homoclinic Orbits to Hyperbolic Equilibria. In: Bifurcation Theory and its Applications in the Scientific Disciplines. Annals of the New York Academy of Sciences 316 (1979), 108-117.

8. Subshifts of Finite Type in Linked Twist Maps. Proceedings of the American Mathematical Society 71 (1978), 334-338.

7. Transverse Heteroclinic Orbits in the Anisotropic Kepler Problem. In: Structure of Attractors in Dynamical Systems. New York: Springer-Verlag (1978), 67-87.

6. Collision Orbits in the Anisotropic Kepler Problem. Inventiones Mathematicae 45 (1978), 221-251.

5. Non-regularizability of the Anisotropic Kepler Problem. Journal of Differential Equations 29 (1978), 253-268.

4. Transversal Homoclinic Orbits in an Integrable System. American Journal of Mathematics 100 (1978), 631-642.

3. Blue Sky Catastrophes in Reversible and Hamiltonian Systems. Indiana University Mathematics Journal 26 (1977), 247-263.

2. Homoclinic Orbits in Hamiltonian Systems. Journal of Differential Equations 21 (1976), 431-438.

1. Reversible Diffeomorphisms and Flows. Transactions of the American Mathematics Society 218 (1976), 89-113.

0. Lens Spaces as Coset Spaces. Pi Mu Epsilon Journal. 5 (1969), 7-11. (Undergrad thesis)

4. Se^x: Dynamics, Topology, and Bifurcations. Topology Conference at C. W. Post College, August, 1999.

3. Cantor Bouquets, Explosions, and Knaster Continua: Dynamics of Complex Exponentials. CRM Lecture Notes. Autonomous University of Barcelona.

2. Fractal Patterns Arising in Dynamical Systems. Course Notes for the SIGGRAPH Summer Course in Fractal Geometry. July, 1987. Also in The Science of Fractal Images. Eds. Peitgen, H. and Saupe, D. New York: Springer-Verlag, 1989. Japanese edition by Springer-Verlag, 1990.

1. Singularities in Classical Mechanical Systems. In Ergodic Theory and Dynamical Systems I. Boston: Birkhauser-Boston, Inc. (1981), 211-333.

11. Chaos, Fractals, and Tom Stoppard's Play, Arcadia. To appear. Abridged online version called Chaos, Fractals, and Arcadia.

10. Unveiling the Mandelbrot set. Plus Magazine, Issue 40, 2006. Online version.

9. Mandelbrot's Vision for Mathematics. In Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot. Proceedings of Symposia in Pure Mathematics. 72 (2004), 39-40.

8. Chaos Rules! Math Horizons, November, 2004, 11-14.

7. Fractal Patterns and Chaos Games. Mathematics Teacher 98 (2004), 228-233.

6. The Dynamical Systems and Technology Project. In ICTCM Proceedings 2004. Pearson Education, 2004.

5. Chaos in the Classroom. In Designing Learning Environments for Developing Understanding of Learning Geometry and Space, eds. R. Lehrer and D. Chazan. Erlbaum Associates (1998), 91-104.

4. Putting Chaos into Calculus Courses. In Discrete Mathematics in the Schools. DIMACS Series in Discrete Mathematics. American Math. Soc. (1997), 239-254. Ed. J. G. Rosenstein, et. al.

3. Explorations in the Chaos Club. Focus. 15 No. 3 (1995), 8-9.

2. Putting Chaos in the Classroom. In NCTM 1991 Yearbook: Discrete Mathematics across the Curriculum, eds. M. Kenney and C. R. Hirsch, NCTM (1991), 184-194.

1. Film and Video as a Tool in Mathematical Research. The Mathematical Intelligencer. 11 No. 2 (1989), 33-38.

16. Chaos in Discrete Dynamical Systems: A Visual Introduction in Two Dimensions. By R. Abraham, et. al. SIAM Review, 40 (1998), 1002-1004.

15. Interactive Differential Equations. By H. Hohn, et. al. American Mathematical Monthly 105 (1998), 687-90.

14. An Introduction to the Modern Theory of Dynamical Systems. By A. Katok and B. Hasselblatt. The Mathematical Intelligencer 20 (1998), 77-78.

13. Interactive Differential Equations. By H. Hohn, et. al. Nonlinear Science, August, 1997.

12. Celestial Encounters. By F. Diacu and P. Holmes. Science 274 (1996), 2032-33.

11. Complex Dynamics. By L. Carleson and T. W. Gamelin, and Rational Iteration. By N. Steinmetz. SIAM Review 36 (1994), 504-505.

10. The General Problem of the Stability of Motion. By A. M. Lyapunov, and Nonlinearities in Action. By A. V. Gaponov-Grekhov and M. I. Rabinovich. Science. 260 (1993), 1173.

9. Chaos, Dynamics and Fractals: An Algorithmic Approach to Deterministic Chaos. By J. L. McCauley. Foundations of Physics.

8. Iteration of Rational Functions. By A. Beardon. American Mathematical Monthly. 100 (1993), 90-93.

7. The Geometer's Sketchpad. Software by N. Jackiw, et.al. UME Trends. 4 No. 2, 1992.

6. Fractals: An Animated Discussion with Edward Lorenz and Benoit Mandelbrot. A Film by H.O. Peitgen, et.al. SIAM Review. 34 (1992), 333-335.

5. Measure, Topology, and Fractal Geometry. By G. Edgar. SIAM Review. 33 (1991), 668-669.

4. Practical Numerical Algorithms for Chaotic Systems. By T.S. Parker and L. Chua. SIAM Review. 32 (1990), 501-503.

3. Global Bifurcations and Chaos. By S. Wiggins. Bulletin of the American Mathematics Society. 20 (1989), 256-259.

2. Chaos: Making a New Science. By James Gleick. SIAM News. September, 1988.

1. Instabilities in Dynamical Systems. Edited by V. Szebehely. Science. 1979.