Escape rates and physical measures for the infinite horizon Lorentz gas with holes

References

• Demers , M F and Young , L -S . 2006 . Escape rates and conditionally invariant measures . Nonlinearity , 19 : 377 – 397 . doi: 10.1088/0951-7715/19/2/008
   Web of Science ®Google Scholar
• Bruin , H , Demers , M F and Melbourne , I . 2010 . Existence and convergence properties of physical measures for certain dynamical systems with holes . Ergod Th Dynam Sys , 30 : 687 – 728 . doi: 10.1017/S0143385709000200
   Web of Science ®Google Scholar
• Čencova , N N . 1981 . A natural invariant measure on Smale’s horseshoe . Sov Math Dokl , 23 : 87 – 91 .
   Google Scholar
• Chernov , N and Markarian , R . 1997 . Ergodic properties of Anosov maps with rectangular holes . Bol Soc Bras Mat , 28 : 271 – 314 . doi: 10.1007/BF01233395
   Google Scholar
• Chernov , N and Markarian , R . 1997 . Anosov maps with rectangular holes . Nonergodic cases. Bol Soc Bras Mat , 28 : 315 – 342 . doi: 10.1007/BF01233396
   Google Scholar
• Chernov , N , Markarian , R and Troubetskoy , S . 1998 . Conditionally invariant measures for Anosov maps with small holes . Ergod Th Dynam Sys , 18 : 1049 – 1073 . doi: 10.1017/S0143385798117492
   Web of Science ®Google Scholar
• Chernov , N , Markarian , R and Troubetskoy , S . 2000 . Invariant measures for Anosov maps with small holes . Ergod Th Dynam Sys , 20 : 1007 – 1044 . doi: 10.1017/S0143385700000560
   Web of Science ®Google Scholar
• Chernov , N and van den , Bedem H . 2002 . Expanding maps of an interval with holes . Ergod Th Dynam Sys , 22 : 637 – 654 .
   Web of Science ®Google Scholar
• Collet , P , Martínez , S and Schmitt , B . 1994 . The Yorke-Pianigiani measure and the asymptotic law on the limit Cantor set of expanding systems . Nonlinearity , 7 : 1437 – 1443 . doi: 10.1088/0951-7715/7/5/010
   Web of Science ®Google Scholar
• Collet , P , Martínez , S and Schmitt , B . 1997 . The Pianigiani-Yorke measure for topological Markov chains . Isr J Math , 97 : 61 – 70 . doi: 10.1007/BF02774026
   Web of Science ®Google Scholar
• Demers , M F . 2005 . Markov extensions for dynamical systems with holes: An application to expanding maps of the interval . Isr J Math , 146 : 189 – 221 . doi: 10.1007/BF02773533
   Web of Science ®Google Scholar
• Demers , M F . 2005 . Markov extensions and conditionally invariant measures for certain logistic maps with small holes . Ergod Th Dynam Sys , 25 ( 4 ) : 1139 – 1171 . doi: 10.1017/S0143385704000963
   Web of Science ®Google Scholar
• Demers , M F and Liverani , C . 2008 . Stability of statistical properties in two-dimensional piecewise hyperbolic maps . Trans Am Math Soc , 360 ( 9 ) : 4777 – 4814 . doi: 10.1090/S0002-9947-08-04464-4
   Web of Science ®Google Scholar
• Liverani , C and Maume-Deschamps , V . 2003 . Lasota-Yorke maps with holes: Conditionally invariant probability measures and invariant probability measures on the survivor set . Ann l’Institut Henri Poincaré Probab Stat , 39 : 385 – 412 . doi: 10.1016/S0246-0203(02)00005-5
   Web of Science ®Google Scholar
• Pianigiani , G and Yorke , J . 1979 . Expanding maps on sets which are almost invariant: Decay and chaos . Trans Am Math Soc , 252 : 351 – 366 .
   Web of Science ®Google Scholar
• Demers , M F . “ Dispersing billiards with small holes ” . In In Ergodic theory, open dynamics and coherent structures. Proceedings in Mathematics , Springer .
   Google Scholar
• Demers , M F , Wright , P and Young , L -S . 2010 . Escape rates and physically relevant measures for billiards with small holes . Comm Math Phys , 294 ( 2 ) : 353 – 388 . doi: 10.1007/s00220-009-0941-y
   Web of Science ®Google Scholar
• Lopes , A and Markarian , R . 1996 . Open Billiards: Cantor sets, invariant and conditionally invariant probabilities . SIAM J Appl Math , 56 : 651 – 680 . doi: 10.1137/S0036139995279433
   Web of Science ®Google Scholar
• Demers , M F and Zhang , H -K . 2011 . Spectral analysis of the transfer operator for the Lorentz gas . J Mod Dyn , 5 ( 4 ) : 665 – 709 . doi: 10.3934/jmd.2011.5.665
   Web of Science ®Google Scholar
• Demers , M F and Zhang , H -K . Spectral analysis for hyperbolic systems with singularities submitted. Available from: http://cs.fairfield.edu/demers/research/pub.html
   Google Scholar
• Chernov , N and Markarian , R . 2006 . Chaotic Billiards , Providence , RI : AMS .
   Google Scholar
• Bunimovich , L , Sinai , Y aG and Chernov , N . 1990 . Markov partitions for two-dimensional hyperbolic billiards . Russ Math Surv , 45 : 105 – 152 . doi: 10.1070/RM1990v045n03ABEH002355
   Web of Science ®Google Scholar
• Keller , G and Liverani , C . 1999 . Stability of the spectrum for transfer operators . Ann Scuola Norm Sup Pisa Cl Sci , 28 ( 4 ) : 141 – 152 .
   Google Scholar
• Demers , M F , Wright , P and Young , L -S . 2012 . Entropy, Lyapunov exponents and escape rates in open systems . Ergod Th Dynam Sys , 32 ( 4 ) : 1270 – 1301 . doi: 10.1017/S0143385711000344
   Web of Science ®Google Scholar
• Katok , A , Strelcyn , J -M , Ledrappier , F . and Przytycki , F . 1986 . “ Invariant Manifolds, Entropy and Billiards; Smooth Maps with Singularities ” . In Lecture Notes in Mathematics , Vol. 1222 , 283 Berlin : Springer-Verlag . with the collaboration of
   Google Scholar
• Hennion , H and Hervé , L . 2001 . Limit Theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness , Berlin : Springer-Verlag .
   Google Scholar
• Chernov , N . 1999 . Decay of correlations and dispersing billiards . J Stat Phys , 94 : 513 – 556 . doi: 10.1023/A:1004581304939
   Web of Science ®Google Scholar