Book Review
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MathSciNet review:
3196802
Full text of review:
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Book Information:
Author:
A. Plakhov
Title:
Exterior billiards: systems with impacts outside bounded domains
Additional book information:
Springer,
New York,
2012,
xiii+284 pp.,
ISBN 978-1-4614-4480-0,
US $109.00
Pavel Bachurin, Konstantin Khanin, Jens Marklof, and Alexander Plakhov, Perfect retroreflectors and billiard dynamics, J. Mod. Dyn. 5 (2011), no. 1, 33–48. MR 2787596, DOI 10.3934/jmd.2011.5.33
M. Berry, Three laws of discovery in http://michaelberryphysics.wordpress.com/quotations/
M. Bialy, A remark on the number of invisible directions for a smooth Riemannian metric, arXiv:1305.2736.
Giuseppe Buttazzo, A survey on the Newton problem of optimal profiles, Variational analysis and aerospace engineering, Springer Optim. Appl., vol. 33, Springer, New York, 2009, pp. 33–48. MR 2573703, DOI 10.1007/978-0-387-95857-6_{3}
Giuseppe Buttazzo and Bernhard Kawohl, On Newton’s problem of minimal resistance, Math. Intelligencer 15 (1993), no. 4, 7–12. MR 1240664, DOI 10.1007/BF03024318
Herman H. Goldstine, A history of the calculus of variations from the 17th through the 19th century, Studies in the History of Mathematics and Physical Sciences, vol. 5, Springer-Verlag, New York-Berlin, 1980. MR 601774
Allan Greenleaf, Yaroslav Kurylev, Matti Lassas, and Gunther Uhlmann, Invisibility and inverse problems, Bull. Amer. Math. Soc. (N.S.) 46 (2009), no. 1, 55–97. MR 2457072, DOI 10.1090/S0273-0979-08-01232-9
Ulf Leonhardt and Thomas Philbin, Geometry and light, Dover Publications, Inc., Mineola, NY, 2010. The science of invisibility. MR 2798945
Isaac Newton, Mathematical principles of natural philosophy. Vol. 1: The motion of bodies, University of California Press, Berkeley-Los Angeles, Calif., 1962. Translated into English by Andrew Motte in 1729; The translations revised, and supplied with an historical and explanatory appendix, by Florian Cajori. MR 0175747
I. Newton, A letter of Mr. Isaac Newton, of the University of Cambridge, containing his new theory about light and color, Philosophical Transactions of the Royal Society 6 (1671), 3075–3087.
Alexander Plakhov, Mathematical retroreflectors, Discrete Contin. Dyn. Syst. 30 (2011), no. 4, 1211–1235. MR 2812962, DOI 10.3934/dcds.2011.30.1211
Alexander Plakhov and Vera Roshchina, Invisibility in billiards, Nonlinearity 24 (2011), no. 3, 847–854. MR 2772626, DOI 10.1088/0951-7715/24/3/007
Alexander Plakhov, Tatiana Tchemisova, and Paulo Gouveia, Spinning rough disc moving in a rarefied medium, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 466 (2010), no. 2119, 2033–2055. MR 2652732, DOI 10.1098/rspa.2009.0518
Serge Tabachnikov, Billiards, Panor. Synth. 1 (1995), vi+142 (English, with English and French summaries). MR 1328336
V. M. Tikhomirov, Stories about maxima and minima, Mathematical World, vol. 1, American Mathematical Society, Providence, RI; Mathematical Association of America, Washington, DC, 1990. Translated from the 1986 Russian original by Abe Shenitzer. MR 1152027
Cédric Villani, Optimal transport, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 338, Springer-Verlag, Berlin, 2009. Old and new. MR 2459454, DOI 10.1007/978-3-540-71050-9
Theme Issue “Flow-control approaches to drag reduction in aerodynamics: progress and prospects”, Phil. Trans. of the Royal Soc. A, 369, 2011.
References
- Pavel Bachurin, Konstantin Khanin, Jens Marklof, and Alexander Plakhov, Perfect retroreflectors and billiard dynamics, J. Mod. Dyn. 5 (2011), no. 1, 33–48. MR 2787596 (2012d:37019), DOI 10.3934/jmd.2011.5.33
- M. Berry, Three laws of discovery in http://michaelberryphysics.wordpress.com/quotations/
- M. Bialy, A remark on the number of invisible directions for a smooth Riemannian metric, arXiv:1305.2736.
- Giuseppe Buttazzo, A survey on the Newton problem of optimal profiles, Variational analysis and aerospace engineering, Springer Optim. Appl., vol. 33, Springer, New York, 2009, pp. 33–48. MR 2573703, DOI 10.1007/978-0-387-95857-6_3
- Giuseppe Buttazzo and Bernhard Kawohl, On Newton’s problem of minimal resistance, Math. Intelligencer 15 (1993), no. 4, 7–12. MR 1240664, DOI 10.1007/BF03024318
- Herman H. Goldstine, A history of the calculus of variations from the 17th through the 19th century, Studies in the History of Mathematics and Physical Sciences, vol. 5, Springer-Verlag, New York, 1980. MR 601774 (83i:01036)
- Allan Greenleaf, Yaroslav Kurylev, Matti Lassas, and Gunther Uhlmann, Invisibility and inverse problems, Bull. Amer. Math. Soc. (N.S.) 46 (2009), no. 1, 55–97. MR 2457072 (2010d:35399), DOI 10.1090/S0273-0979-08-01232-9
- Ulf Leonhardt and Thomas Philbin, Geometry and light. The science of invisibility, Dover Publications Inc., Mineola, NY, 2010. MR 2798945 (2012f:53001)
- Isaac Newton, Mathematical principles of natural philosophy. Vol. 1: The motion of bodies, Translated into English by Andrew Motte in 1729. The translations revised, and supplied with an historical and explanatory appendix, by Florian Cajori, University of California Press, Berkeley, 1962. MR 0175747 (31 \#24a)
- I. Newton, A letter of Mr. Isaac Newton, of the University of Cambridge, containing his new theory about light and color, Philosophical Transactions of the Royal Society 6 (1671), 3075–3087.
- Alexander Plakhov, Mathematical retroreflectors, Discrete Contin. Dyn. Syst. 30 (2011), no. 4, 1211–1235. MR 2812962 (2012f:37080), DOI 10.3934/dcds.2011.30.1211
- Alexander Plakhov and Vera Roshchina, Invisibility in billiards, Nonlinearity 24 (2011), no. 3, 847–854. MR 2772626 (2012a:37072), DOI 10.1088/0951-7715/24/3/007
- Alexander Plakhov, Tatiana Tchemisova, and Paulo Gouveia, Spinning rough disc moving in a rarefied medium, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 466 (2010), no. 2119, 2033–2055. MR 2652732 (2011j:76152), DOI 10.1098/rspa.2009.0518
- Serge Tabachnikov, Billiards, Panor. Synth. 1 (1995), vi+142 (English, with English and French summaries). MR 1328336 (96c:58134)
- V. M. Tikhomirov, Stories about maxima and minima, Mathematical World, vol. 1, American Mathematical Society, Providence, RI, 1990. Translated from the 1986 Russian original by Abe Shenitzer. MR 1152027 (92k:49002)
- Cédric Villani, Optimal transport: old and new, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 338, Springer-Verlag, Berlin, 2009. MR 2459454 (2010f:49001), DOI 10.1007/978-3-540-71050-9
- Theme Issue “Flow-control approaches to drag reduction in aerodynamics: progress and prospects”, Phil. Trans. of the Royal Soc. A, 369, 2011.
Review Information:
Reviewer:
Serge Tabachnikov
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania
Email:
tabachni@math.psu.edu
Journal:
Bull. Amer. Math. Soc.
51 (2014), 519-526
DOI:
https://doi.org/10.1090/S0273-0979-2014-01452-1
Published electronically:
March 11, 2014
Additional Notes:
Supported by the NSF grant DMS-1105442.
Review copyright:
© Copyright 2014
American Mathematical Society
