- Fractal basins and chaotic trajectories in multi-black-hole space-times. C. P. Dettmann, N. E. Frankel and N. J. Cornish, Phys. Rev. D,
**50,**R618-R621 (1994) pdf arxiv - Chaos and fractals around black holes C. P. Dettmann, N. E. Frankel and N. J. Cornish, Fractals
**3**161-181 (1995) pdf arxiv - Chaos in special relativistic dynamics S. Drake, C. P. Dettmann, N. E. Frankel and N. J. Cornish, Phys. Rev. E
**53,**1351-1361 (1996) pdf - Self-similar magnetoresistance of a semiconductor Sinai billiard, R. P. Taylor, R. Newbury, A. S. Sachrajda, Y. Feng, P. T. Coleridge, C. P. Dettmann, N. Zhu, H. Guo, A. Delage, P. J. Kelly and Z. Wasilewski, Phys. Rev. Lett.,
**78,**1952-1955 (1997) pdf ps[Physical experiment demonstrating tunable chaos and self-similar magnetoresistance fluctuations] - Fractal behavior in the magnetoresistance of chaotic billiards, R. Newbury, R. P. Taylor, A. S. Sachrajda, Y. Feng, P. T. Coleridge, C. P. Dettmann and T. M. Fromhold, Jpn. J. Appl. Phys.
**36,**3991-3995 (1997) - Fractal transistors, R. P. Taylor, A. P. Micolich, R. Newbury, C. P. Dettmann and T. M. Fromhold, Semicond. Sci. Tech.
**12,**1459-1464 (1997) - Geometry-induced fractal behavior in a semiconductor billiard, A. P. Micolich, R. P. Taylor, R. Newbury, J. P. Bird, R. Wirtz, C. P. Dettmann, Y. Aoyagi and T. Sugano, J. Phys.: Cond. Mat.
**10,**1339-1347 (1998) - Experimental and theoretical investigations of clusters in the magneto-fingerprints of Sinai billiards, R. P. Taylor, A. P. Micolich, R. Newbury, T. M. Fromhold, C. P. Dettmann and C. R. Tench, Mat. Sci. Eng. B
**51,**212-215 (1998) - Experimental and theoretical investigations of electron dynamics in a semiconductor Sinai billiard, A. P. Micolich, R. P. Taylor, R. Newbury, C. P. Dettmann and T. M. Fromhold, Aust. J. Phys.
**51,**547-555 (1998) - Trace formulas for stochastic evolution operators: Weak noise perturbation theory P. Cvitanovic', C. P. Dettmann, R. Mainieri, and G. Vattay, J. Stat. Phys.
**93,**981-999 (1998) ps.gz (1.2M when uncompressed) arxiv - Traces and determinants of strongly stochastic operators C. P. Dettmann, Phys. Rev. E
**59,**5231-5234 (1999) pdf ps html arxiv - Trace formulas for stochastic evolution operators: Smooth conjugation method P. Cvitanovic', C. P. Dettmann, R. Mainieri, and G. Vattay, Nonlinearity
**12,**939-953 (1999) ps arxiv - Spectrum of stochastic evolution operators: Local matrix representation approach P. Cvitanovic', N. Sondergaard, G. Palla, G. Vattay, and C. P. Dettmann, Phys. Rev. E
**60,**3936-3941 (1999) pdf ps Two distinct arxiv versions:arxiv arxiv - Microscopic chaos and diffusion C. P. Dettmann and E. G. D. Cohen, J. Stat. Phys.
**101,**775-817 (2000) ps.gz (28 pages; 2.1M when uncompressed) arxiv - Noise corrections to stochastic trace formulas G. Palla, G. Vattay, A. Voros, N. Sondergaard, C. P. Dettmann, Found. Phys.
**31,**641-657 (2001). arxiv - Fractal asymptotics, C. P. Dettmann, Physica D
**187,**214-222 (2004). ps arxiv - Open circular billiards and the Riemann hypothesis, L. A. Bunimovich and C. P. Dettmann, Phys. Rev. Lett.
**94**100201 (2005) ps pdf RH day slides - Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape rates L. A. Bunimovich and C. P. Dettmann, EPL,
**80**40001 (2007). pdf arxivanimation (6.1M) - Directional emission from an optical microdisk resonator with a point scatterer C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, EPL,
**82**34002 (2008). pdf arxiv - Internal and external resonances of dielectric disks, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, EPL,
**87**, 34003 (2009). pdf arxiv - Survival probability for the stadium billiard, C. P. Dettmann and O. Georgiou, Physica D,
**238**, 2395-2403 (2009). pdf arxiv animation (30.5M) - Unidirectional Emission from Circular Dielectric Microresonators with a Point Scatterer, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, Phys. Rev. A,
**80**, 063813 (2009). [Selected to appear in the PRA "Kaleidoscope"] pdf arxiv poster - Transmission and reflection in the stadium billiard: Time-dependent asymmetric transport, C. P. Dettmann and O. Georgiou, Phys. Rev. E
**83**036212 (2011). [Selected to appear in the PRE "Kaleidoscope"] pdf arxiv poster - Open mushrooms: Stickiness revisited, C. P. Dettmann and O. Georgiou, J. Phys. A.: Math. Theor.
**44**195102 (2011). [Highlighted in a JPA Insights article.] pdf arxiv poster - Escape of particles in a time-dependent potential well, D. R. Costa, C. P. Dettmann and E. D. Leonel, Phys. Rev. E,
**83**066211 (2011). pdf - Scaling invariance for the escape of particles from a periodically corrugated waveguide, E. D. Leonel, D. R. Costa and C. P. Dettmann, Phys. Lett. A
**376**421-425 (2012). pdf - New horizons in multidimensional diffusion: The Lorentz gas and the Riemann Hypothesis, C. P. Dettmann, J. Stat. Phys.
**146**181-204 (2012). pdf arxiv animation (4.8M) - Escape and transport for an open bouncer: Stretched exponential decays, C. P. Dettmann and E. D. Leonel, Physica D
**241**403-408 (2012). pdf arxiv - Recurrence of particles in static and time varying oval billiards, E. D. Leonel and C. P. Dettmann, Phys. Lett. A
**376**1669-1674 (2012). pdf arxiv - Dependence of chaotic diffusion on the size and position of holes, G. Knight, O. Georgiou, C. P. Dettmann, R. Klages, Chaos
**22**023132 (2012). pdf arxiv - Quantifying intermittency in the open drivebelt billiard, C. P. Dettmann and O. Georgiou, Chaos
**22**026113 (2012). pdf arxiv - Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration, A. L. P. Livorati, T. Kroetz, C. P. Dettmann, I. L. Caldas, E. D. Leonel, Phys. Rev. E
**86**036203 (2012). pdf arxiv - Faster than expected escape for a class of fully chaotic maps, O. Georgiou, C. P. Dettmann, E. G. Altmann, Chaos
**22**043115 (2012). arxiv pdf - Open circle maps: Small hole asymptotics, C. P. Dettmann, Nonlinearity
**26**307-317 (2013). pdf arxiv - Scaling invariance of the diffusion coefficient in a family of two-dimensional Hamiltonian mappings, J. A. de Oliveira, C. P. Dettmann, D. R. Costa and E. D. Leonel, Phys. Rev. E
**87**062904 (2013). pdf - Escape through a time-dependent hole in the doubling map, A. L. P. Livorati, O. Georgiou, C. P. Dettmann and E. D. Leonel, Phys. Rev. E,
**89**052913 (2014). arxiv pdf - Survival probability for open spherical billiards, C. P. Dettmann and M. R. Rahman, Chaos
**24**043130 (2014). arxiv pdf - Network connectivity in non-convex domains with reflections, O. Georgiou, M. Z. Bocus, M. R. Rahman, C. P. Dettmann and J. P. Coon, IEEE Commun. Lett.
**19**427-430 (2015). pdf arxiv. - Universal hitting time statistics for integrable flows, C. P. Dettmann, J. Marklof and A. Strombergsson, J. Stat. Phys.
**166**714-749 (2017). arxiv pdf. - Conference paper: Far-field emission pattern of a dielectric circular microresonator with a point scatterer, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, ICTON 2007,
**4**197-200 (2007) - Conference paper: TM and TE directional modes of an optical microdisk resonator with a point scatterer, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, ICTON 2008,
**4**, 65-68 (2008). pdf - Conference paper: Optical microdisk resonator with a small but finite size scatterer, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, Third International Conference on Mathematical Modelling of Wave Phenomena (MMWP08), 287-289 (2008). pdf
- Conference paper: Systematization of All Resonance Modes in Circular Dielectric Cavities, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, ICTON 2009, 763-766 (2009). pdf
- Conference paper: Microdisk resonators with two point scatterers, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, ICTON 2011, 462-464 (2011). pdf
- Conference paper: How sticky is the chaos/order boundary? C. P. Dettmann, Contemporary Mathematics
**698**111-128 (2017). pdf arxiv. - Book chapter: The Lorentz gas as a paradigm for nonequilibrium stationary states, C. P. Dettmann, pp 315-365 in Hard ball systems and the Lorentz gas (edited by D. Szasz), Encyclopaedia of Mathematical Sciences Vol 101 (Springer, 2000). Full size version, 50 pages pdf. Environmental microscopic version, 25 pages pdf.
- Book chapter: Recent advances in open billiards with some open problems, C. P. Dettmann, in Frontiers in the study of chaotic dynamical systems with open problems (Ed. Z. Elhadj and J. C. Sprott, World Scientific, 2011) arxiv [Image featured in Plus magazine]

Measuring the escape of particles through the boundaries of the system is often a fruitful approach to understanding the dynamics. Examples include fractal basin boundaries in relativistic systems, fractal conductance fluctuations in semiconductor billiards, the effects of stochastic perturbations on the escape rate, and connections with number theory in escape from integrable systems including microresonators.

Recent work has focused on billiards, with some surprising results: in the simplest possible geometry, the integrable circle, the escape is related to the Riemann Hypothesis. An intermittent system, the stadium billiard, exhibits asymmetric transport, with the time-dependence of the probability of remaining in the system being exponential (rapid) or algebraic (slow) depending on the holes through which the particle passes. This shows that open systems can behave very differently to their closed counterparts, and also leads to some interesting questions in the corresponding quantum/wave problems.

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