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Forced linear oscillators and the dynamics of Euclidean group extensions
1. | Department of Mathematics, Rutgers University, Camden NJ 08102, United States |
References:
[1] |
A. Avila, G. Forni and C. Ulcigrai, Mixing for time changes of Heisenberg nil flows, J. of Diff Geometry, 89 (2011), 369-410. |
[2] |
D. Anosov and A. Katok, New examples in smooth ergodic theory, Trans. Moscow Math. Soc., 23 (1970), 1-35. |
[3] |
P. Ashwin and I. Melbourne, Non-compact drft for relative equillibria and relative periodic orbits, Nonlinearity, 10 (1997), 595-616.
doi: 10.1088/0951-7715/10/3/002. |
[4] |
P. Ashwin, I. Melbourne and M. Nicol, Euclidean extensions of dynamical systems, Nonlinearity, 14 (2001), 275-300.
doi: 10.1088/0951-7715/14/2/306. |
[5] |
J. Bellisard, Stability and instability in quantum mechanics, Trends and developments in the eighties (Bielefeld, 1982/1983), World Sci. Publishing, Singapore, 1985, 1-106. |
[6] |
L. Bunimovich, H. Jauslin, J. Lebowitz, A. Pellegrinoti and P. Nilaba, Diffusive energy growth in classical and quantum driven oscillators, Journal of Statistical Physics, 62 (1991), 793-817.
doi: 10.1007/BF01017984. |
[7] |
M. Combescure, Recurrent versus diffusive dynamics for a kicked quantum oscillator, Annales de l'Institute Henri Poincaré (A) Physique Theorique, 57 (1992), 67-87. |
[8] |
M. Fields, I. Melbourne and M. Nicol, Symmetric attractors for diffeomorphisms and flows, Proc. London Math. Soc., 72 (1996), 657-696.
doi: 10.1112/plms/s3-72.3.657. |
[9] |
S. Glasner and B. Weiss, On the construction of minimal skew products, Israel J. Math., 34 (1979), 321-336.
doi: 10.1007/BF02760611. |
[10] |
M. Herman, Construction de diffeomorphismes ergodiques,, preprint., ().
|
[11] |
R. Johnson and M. Nerurkar, On null Controllability of linear systems with recurrent coefficients and constrained controls, (jointly with R. Johnson), Journal of Dynamics and Differential Equations, 4 (1992), 259-273.
doi: 10.1007/BF01049388. |
[12] |
H. Keynes and D. Newton, Ergodicity in $(G,\sigma )$ extensions, Springer Verlag Lecture Note in Math., 668 (1978), 173-178. |
[13] |
J. Lebowitz and H. Jauslin, Spectral and stability aspects of quantum chaos, Chaos, 1 (1991), 114-121.
doi: 10.1063/1.165809. |
[14] |
E. Lesigne and D. Volny, Large deviations for generic stationary processes, Colloquium Mathematicum, 84/85 (2000), 75-82. |
[15] |
E. Merzbacher, Quantum Mechanics, 5th edition, Wiley, New York, 1965. |
[16] |
I. Melbourne, V. Nitica and A. Torok, Transitivity of Euclidean type extensions of hyperbolic systems, Ergodic Theory and Dynamical Systems, 29 (2009), 1582-1602.
doi: 10.1017/S0143385708000886. |
[17] |
M. Nerurkar, On the construction of smooth ergodic skew products, Ergodic Theory and Dynamical Systems, 8 (1988), 311-326.
doi: 10.1017/S0143385700004454. |
[18] |
M. Nerurkar, Spectral and stability questions regarding evolution of non-autonomous linear systems, J. of Discrete and Continuous Dynamical Systems, (2004), 114-120. |
[19] |
M. Nerurkar and H. Jauslin, Stability of oscillators driven by ergodic processes, J. of Math. physics, 35 (1994), 628-645.
doi: 10.1063/1.530657. |
[20] |
M. Nerurkar and H. Sussmann, Construction of minimal cocycles arising from specific differential equations, (jointly with H. Sussmann), Israel Journal of Mathematics, 100 (1997), 309-326.
doi: 10.1007/BF02773645. |
[21] |
M. Nerurkar and H. Sussmann, Construction of ergodic cocycles arising from linear differential equations of special form, Journal of Modern Dynamics, 1 (2007), 205-253.
doi: 10.3934/jmd.2007.1.205. |
[22] |
V. Nitica and M. Pollicott, Transitivity of Euclidean group extensions of Anosov diffeomorphisms, Ergodic Theory and Dynamical Systems, 25 (2005), 257-269.
doi: 10.1017/S0143385704000471. |
[23] |
K. Schmidt, Cocycles and Ergodic Transformation Groups, MacMillan of India, 1977. |
show all references
References:
[1] |
A. Avila, G. Forni and C. Ulcigrai, Mixing for time changes of Heisenberg nil flows, J. of Diff Geometry, 89 (2011), 369-410. |
[2] |
D. Anosov and A. Katok, New examples in smooth ergodic theory, Trans. Moscow Math. Soc., 23 (1970), 1-35. |
[3] |
P. Ashwin and I. Melbourne, Non-compact drft for relative equillibria and relative periodic orbits, Nonlinearity, 10 (1997), 595-616.
doi: 10.1088/0951-7715/10/3/002. |
[4] |
P. Ashwin, I. Melbourne and M. Nicol, Euclidean extensions of dynamical systems, Nonlinearity, 14 (2001), 275-300.
doi: 10.1088/0951-7715/14/2/306. |
[5] |
J. Bellisard, Stability and instability in quantum mechanics, Trends and developments in the eighties (Bielefeld, 1982/1983), World Sci. Publishing, Singapore, 1985, 1-106. |
[6] |
L. Bunimovich, H. Jauslin, J. Lebowitz, A. Pellegrinoti and P. Nilaba, Diffusive energy growth in classical and quantum driven oscillators, Journal of Statistical Physics, 62 (1991), 793-817.
doi: 10.1007/BF01017984. |
[7] |
M. Combescure, Recurrent versus diffusive dynamics for a kicked quantum oscillator, Annales de l'Institute Henri Poincaré (A) Physique Theorique, 57 (1992), 67-87. |
[8] |
M. Fields, I. Melbourne and M. Nicol, Symmetric attractors for diffeomorphisms and flows, Proc. London Math. Soc., 72 (1996), 657-696.
doi: 10.1112/plms/s3-72.3.657. |
[9] |
S. Glasner and B. Weiss, On the construction of minimal skew products, Israel J. Math., 34 (1979), 321-336.
doi: 10.1007/BF02760611. |
[10] |
M. Herman, Construction de diffeomorphismes ergodiques,, preprint., ().
|
[11] |
R. Johnson and M. Nerurkar, On null Controllability of linear systems with recurrent coefficients and constrained controls, (jointly with R. Johnson), Journal of Dynamics and Differential Equations, 4 (1992), 259-273.
doi: 10.1007/BF01049388. |
[12] |
H. Keynes and D. Newton, Ergodicity in $(G,\sigma )$ extensions, Springer Verlag Lecture Note in Math., 668 (1978), 173-178. |
[13] |
J. Lebowitz and H. Jauslin, Spectral and stability aspects of quantum chaos, Chaos, 1 (1991), 114-121.
doi: 10.1063/1.165809. |
[14] |
E. Lesigne and D. Volny, Large deviations for generic stationary processes, Colloquium Mathematicum, 84/85 (2000), 75-82. |
[15] |
E. Merzbacher, Quantum Mechanics, 5th edition, Wiley, New York, 1965. |
[16] |
I. Melbourne, V. Nitica and A. Torok, Transitivity of Euclidean type extensions of hyperbolic systems, Ergodic Theory and Dynamical Systems, 29 (2009), 1582-1602.
doi: 10.1017/S0143385708000886. |
[17] |
M. Nerurkar, On the construction of smooth ergodic skew products, Ergodic Theory and Dynamical Systems, 8 (1988), 311-326.
doi: 10.1017/S0143385700004454. |
[18] |
M. Nerurkar, Spectral and stability questions regarding evolution of non-autonomous linear systems, J. of Discrete and Continuous Dynamical Systems, (2004), 114-120. |
[19] |
M. Nerurkar and H. Jauslin, Stability of oscillators driven by ergodic processes, J. of Math. physics, 35 (1994), 628-645.
doi: 10.1063/1.530657. |
[20] |
M. Nerurkar and H. Sussmann, Construction of minimal cocycles arising from specific differential equations, (jointly with H. Sussmann), Israel Journal of Mathematics, 100 (1997), 309-326.
doi: 10.1007/BF02773645. |
[21] |
M. Nerurkar and H. Sussmann, Construction of ergodic cocycles arising from linear differential equations of special form, Journal of Modern Dynamics, 1 (2007), 205-253.
doi: 10.3934/jmd.2007.1.205. |
[22] |
V. Nitica and M. Pollicott, Transitivity of Euclidean group extensions of Anosov diffeomorphisms, Ergodic Theory and Dynamical Systems, 25 (2005), 257-269.
doi: 10.1017/S0143385704000471. |
[23] |
K. Schmidt, Cocycles and Ergodic Transformation Groups, MacMillan of India, 1977. |
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