Impenetrable barriers in phase space for deterministic thermostats

Journal of Physics A: Mathematical and Theoretical

Volumn 42, Issue 4, 2009, Pages

  Ezra, Gregory S ^a   Wiggins, Stephen ^b  

^a Department of Obstetrics Gynecology   (United States)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 64549121162     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/42/4/042001     Document Type: Article

References (66)

1. Nosé S 1991 Prog. Theor. Phys. Suppl. 103 1
2. Morriss G P and Dettmann C P 1998 Chaos 8 321
3. Leimkuhler B and Reich S 2004 Simulating Hamiltonian Dynamics (Cambridge: Cambridge University Press)
4. Hunenberger P 2005 Adv. Polym. Sci. 173 105
5. Bond S D and Leimkuhler B J 2007 Acta Numer. 16 1
6. Nosé S 1984 J. Chem. Phys. 81 511
7. Hoover W G 1985 J. Chem. Phys. 31 1695
8. Dettmann C P and Morriss G P 1996 Phys. Rev. E 54 2495
9. Dettmann C P and Morriss G P 1997 Phys. Rev. E 55 3693
10. Dettmann C P 1999 Phys. Rev. E 60 7576
11. Bond S D, Leimkuhler B J and Laird B B 1999 J. Comput. Phys. 151 114
12. Evans D J and Morriss G P 1990 Statistical Mechanics of Nonequilibrium Liquids (New York: Academic)
13. Tuckerman M E, Mundy C J and Martyna G J 1999 Europhys. Lett. 45 149
14. Tuckerman M E, Liu Y, Ciccotti G and Martyna G J 2001 J. Chem. Phys. 115 1678
15. Sergi A and Ferrario M 2001 Phys. Rev. E 64 056125
16. Sergi A 2003 Phys. Rev. E 67 021101
17. Ezra G S 2004 J. Math. Chem. 35 29
18. Tarasov V E 2005 J. Phys. A: Math. Gen. 38 2145
19. Ezra G S 2006 J. Chem. Phys. 125 034104
20. Sergi A and Giaquinta P V 2007 J. Stat. Mech. P02013
21. Sanz-Serna J M and Calvo M P 1994 Numerical Hamiltonian Problems (London: Chapman and Hall)
22. Hairer E, Lubich C and Wanner G 2002 Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations (New York: Springer)
23. Bond S D and Leimkuhler B J 1998 Numer. Algorithms 19 55
24. Benest D and Froeschlé C ed 2002 Singularities in Gravitational Systems: Applications to Chaotic Transport in the Solar System (New York: Springer)
25. Cornfeld I P, Fomin S V and Sinai Y G 1982 Ergodic Theory (New York: Springer)
26. Sturman R, Ottino J M and Wiggins S 2006 The Mathematical Foundations of Mixing (Cambridge: Cambridge University Press)
27. Legoll F, Luskin M and Moeckel R 2007 Arch. Ration. Mech. Anal. 184 449
28. Martyna G J, Klein M L and Tuckerman M E 1992 J. Chem. Phys. 97 2635
29. Leimkuhler B J and Sweet C R 2005 SIAM J. Appl. Dyn. Syst. 4 187
30. Robinson P J and Holbrook K A 1972 Unimolecular Reactions (New York: Wiley)
31. Gilbert R G and Smith S C 1990 Theory of Unimolecular and Recombination Reactions (Oxford: Blackwell)
32. Baer T and Hase W L 1996 Unimolecular Reaction Dynamics (Oxford: Oxford University Press)
33. DeLeon N and Berne B J 1981 J. Chem. Phys. 75 3495
34. Carpenter B K 2005 Ann. Rev. Phys. Chem. 56 57
35. Wiggins S 1990 Physica D 44 471
36. Wiggins S 1992 Chaotic Transport in Dynamical Systems (Berlin: Springer)
37. Wiggins S 1994 Normally Hyperbolic Invariant Manifolds in Dynamical Systems (Berlin: Springer)
38. Wiggins S, Wiesenfeld L, Jaffe C and Uzer T 2001 Phys. Rev. Lett. 86 5478
39. Waalkens H, Schubert R and Wiggins S 2008 Nonlinearity 21 R1
40. Pechukas P 1981 Ann. Rev. Phys. Chem. 32 159
41. Posch H A, Hoover W G and Vesely F J 1986 Phys. Rev. A 33 4253
42. Posch H A and Hoover W G 1997 Phys. Rev. E 55 6803
43. Hoover W G 1998 J. Chem. Phys. 109 4164
44. Hoover W G, Hoover C G and Isbister D J 2001 Phys. Rev. E 63 026209
45. Martens C C, Davis M J and Ezra G S 1987 Chem. Phys. Lett. 142 519
46. Laskar J 1993 Physica D 67 257
47. Vela-Arevalo L V and Wiggins S 2001 Int. J. Bifurcation Chaos 11 1359
48. Minary P, Martyna G J and Tuckerman M E 2003 J. Chem. Phys. 118 2510
49. Minary P, Martyna G J and Tuckerman M E 2003 J. Chem. Phys. 118 2527
50. Litniewski M 1993 J. Phys. Chem. 97 3842
51. Morishita T 2003 J. Chem. Phys. 119 7075
52. Uzer T, Jaffe C, Palacian J, Yanguas P and Wiggins S 2002 Nonlinearity 15 957
53. Waalkens H, Burbanks A and Wiggins S 2004 J. Phys. A: Math. Gen. 37 L257
54. Waalkens H and Wiggins S 2004 J. Phys. A: Math. Gen. 37 L435
55. Waalkens H, Burbanks A and Wiggins S 2004 J. Chem. Phys. 121 6207
56. Waalkens H, Burbanks A and Wiggins S 2005 Phys. Rev. Lett. 95 084301
57. Waalkens H, Burbanks A and Wiggins S 2005 J. Phys. A: Math. Gen. 38 L759
58. Schubert R, Waalkens H and Wiggins S 2006 Phys. Rev. Lett. 96 218302
59. Truhlar D G, Garrett B C and Klippenstein S J 1996 J. Phys. Chem. 100 12771
60. Heidrich D 1995 The Reaction Path in Chemistry: Current Approaches and Perspectives (Boston: Kluwer)
61. Arnold V I 1978 Mathematical Methods of Classical Mechanics (New York: Springer)
62. Maslov V P and Fedoryuk M V 1981 Semiclassical Approximations in Quantum Mechanics (Boston: Reidel)
63. Littlejohn R G 1992 J. Stat. Phys. 68 7
64. Silvester J R 2000 Math. Gaz. 84 460
65. de la Llave R 1992 Commun. Math. Phys. 150 289
66. Fontich E, de la Llave R and Martín P 2006 Trans. Am. Math. Soc. 358 1317