Intermittent quasistatic dynamical systems: weak convergence of fluctuations

Intermittent quasistatic dynamical systems: weak convergence of fluctuations References[1] Romain Aimino, Huyi Hu, Matthew Nicol, Andrei Török, and Sandro Vaienti. Polynomial loss of memory for maps of the interval with a neutral fixed point. Discrete Contin. Dyn. Syst., 35(3):793-806, 2015. URL: http://dx.doi.org/10.3934/dcds. 2015.35.793.10.3934/dcds.2015.35.793[2] Romain Aimino and Jérôme Rousseau. Concentration inequalities for sequential dynamical systems of the unit interval. Ergodic Theory Dynam. Systems, 36(8):2384-2407, 2016. URL: http://dx.doi.org/10.1017/etds.2015.19.[3] Wael Bahsoun and Christopher Bose. Mixing rates and limit theorems for random intermittent maps. Nonlinearity, 29(4):1417-1433, 2016. URL: http://dx.doi.org/10.1088/0951-7715/29/4/1417.10.1088/0951-7715/29/4/1417[4] Wael Bahsoun, Christopher Bose, and Yuejiao Duan. Decay of correlation for random intermittent maps. Nonlinearity, 27(7):1543-1554, 2014. URL: http://dx.doi.org/10.1088/0951-7715/27/7/1543.10.1088/0951-7715/27/7/1543[5] Wael Bahsoun, Christopher Bose, and Marks Ruziboev. Quenched decay of correlations for slowly mixing systems. 2017. Preprint. arXiv:1706.04158.[6] Wael Bahsoun, Marks Ruziboev, and Benoît Saussol. Linear response for random dynamical systems. 2017. Preprint. arXiv:1710.03706.[7] Jean-Pierre Conze and Albert Raugi. Limit theorems for sequential expanding dynamical systems on [0, 1]. In Ergodic theory and related fields, volume 430 of Contemp. Math., pages 89-121. Amer. Math. Soc., Providence, RI, 2007. doi: 10.1090/conm/430/08253.[8] Neil Dobbs and Mikko Stenlund. Quasistatic dynamical systems. 2016. To appear in Ergodic Theory and Dynamical Systems. doi:10.1017/etds.2016.9.[9] Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, and Sandro Vaienti. Extreme value laws for sequences of intermittent maps. 2017. Preprint. arXiv:1605.06287.[10] Chinmaya Gupta, William Ott, and Andrei Török. Memory loss for time-dependent piecewise expanding systems in higher dimension. Math. Res. Lett., 20(1):141-161, 2013. doi:10.4310/MRL.2013.v20.n1.a12.[11] Nicolai Haydn, Matthew Nicol, Andrew Török, and Sandro Vaienti. Almost sure invariance principle for sequential and nonstationary dynamical systems. Trans. Amer. Math. Soc., 369(8):5293-5316, 2017. doi:10.1090/tran/6812.[12] Christoph Kawan. Metric entropy of nonautonomous dynamical systems. Nonauton. Dyn. Syst., 1:26-52, 2014. doi:10. 2478/msds-2013-0003.[13] Christoph Kawan. Expanding and expansive time-dependent dynamics. Nonlinearity, 28(3):669-695, 2015. doi:10.1088/0951-7715/28/3/669.[14] Alexey Korepanov, Zemer Kosloff, and Ian Melbourne. Martingale-coboundary decomposition for families of dynamical systems. 2016. Preprint. arXiv:1608.01853.[15] Juho Leppänen and Mikko Stenlund. Quasistatic dynamics with intermittency. Math. Phys. Anal. Geom., 19(2):Art. 8, 23, 2016. URL: http://dx.doi.org/10.1007/s11040-016-9212-2.10.1007/s11040-016-9212-2[16] Juho Leppänen. Functional correlation decay and multivariate normal approximation for non-uniformly expanding maps. Nonlinearity, 30(11):4239, 2017. URL: http://stacks.iop.org/0951-7715/30/i=11/a=4239.[17] Carlangelo Liverani, Benoît Saussol, and Sandro Vaienti. A probabilistic approach to intermittency. Ergodic Theory Dynam. Systems, 19(3):671-685, 1999. URL: http://dx.doi.org/10.1017/S0143385799133856.10.1017/S0143385799133856[18] Anushaya Mohapatra andWilliam Ott. Memory loss for nonequilibriumopen dynamical systems. Discrete Contin. Dyn. Syst., 34(9):3747-3759, 2014. doi:10.3934/dcds.2014.34.3747.[19] Péter Nándori, Domokos Szász, and Tamás Varjú. A central limit theorem for time-dependent dynamical systems. J. Stat. Phys., 146(6):1213-1220, 2012. doi:10.1007/s10955-012-0451-8.[20] Matthew Nicol, Andrew Török, and Sandro Vaienti. Central limit theorems for sequential and random intermittent dynamical systems. 2016. To appear in Ergodic Theory and Dynamical Systems. doi:10.1017/etds.2016.69.[21] William Ott, Mikko Stenlund, and Lai-Sang Young. Memory loss for time-dependent dynamical systems. Math. Res. Lett., 16(3):463-475, 2009. doi:10.4310/MRL.2009.v16.n3.a7.[22] L. C. G. Rogers and David Williams. Diffusions, Markov processes, and martingales. Vol. 2. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 2000. Itô calculus, Reprint of the second (1994) edition. doi:10.1017/ CBO9781107590120.[23] Mikko Stenlund. A vector-valued almost sure invariance principle for Sinai billiards with random scatterers. Comm. Math. Phys., 325(3):879-916, 2014. doi:10.1007/s00220-013-1870-3.[24] Mikko Stenlund. An almost sure ergodic theorem for quasistatic dynamical systems. Math. Phys. Anal. Geom., 19(3):Art. 14, 18, 2016. doi:10.1007/s11040-016-9217-x.[25] Matteo Tanzi, Tiago Pereira, and Sebastian van Strien. Robustness of ergodic properties of nonautonomous piecewise expanding maps. 2016. Preprint. arXiv:1611.04016. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonautonomous and Stochastic Dynamical Systems de Gruyter

Intermittent quasistatic dynamical systems: weak convergence of fluctuations

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de Gruyter
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© 2018
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2299-3258
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2353-0626
D.O.I.
10.1515/msds-2018-0002
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Abstract

References[1] Romain Aimino, Huyi Hu, Matthew Nicol, Andrei Török, and Sandro Vaienti. Polynomial loss of memory for maps of the interval with a neutral fixed point. Discrete Contin. Dyn. Syst., 35(3):793-806, 2015. URL: http://dx.doi.org/10.3934/dcds. 2015.35.793.10.3934/dcds.2015.35.793[2] Romain Aimino and Jérôme Rousseau. Concentration inequalities for sequential dynamical systems of the unit interval. Ergodic Theory Dynam. Systems, 36(8):2384-2407, 2016. URL: http://dx.doi.org/10.1017/etds.2015.19.[3] Wael Bahsoun and Christopher Bose. Mixing rates and limit theorems for random intermittent maps. Nonlinearity, 29(4):1417-1433, 2016. URL: http://dx.doi.org/10.1088/0951-7715/29/4/1417.10.1088/0951-7715/29/4/1417[4] Wael Bahsoun, Christopher Bose, and Yuejiao Duan. Decay of correlation for random intermittent maps. Nonlinearity, 27(7):1543-1554, 2014. URL: http://dx.doi.org/10.1088/0951-7715/27/7/1543.10.1088/0951-7715/27/7/1543[5] Wael Bahsoun, Christopher Bose, and Marks Ruziboev. Quenched decay of correlations for slowly mixing systems. 2017. Preprint. arXiv:1706.04158.[6] Wael Bahsoun, Marks Ruziboev, and Benoît Saussol. Linear response for random dynamical systems. 2017. Preprint. arXiv:1710.03706.[7] Jean-Pierre Conze and Albert Raugi. Limit theorems for sequential expanding dynamical systems on [0, 1]. In Ergodic theory and related fields, volume 430 of Contemp. Math., pages 89-121. Amer. Math. Soc., Providence, RI, 2007. doi: 10.1090/conm/430/08253.[8] Neil Dobbs and Mikko Stenlund. Quasistatic dynamical systems. 2016. To appear in Ergodic Theory and Dynamical Systems. doi:10.1017/etds.2016.9.[9] Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, and Sandro Vaienti. Extreme value laws for sequences of intermittent maps. 2017. Preprint. arXiv:1605.06287.[10] Chinmaya Gupta, William Ott, and Andrei Török. Memory loss for time-dependent piecewise expanding systems in higher dimension. Math. Res. Lett., 20(1):141-161, 2013. doi:10.4310/MRL.2013.v20.n1.a12.[11] Nicolai Haydn, Matthew Nicol, Andrew Török, and Sandro Vaienti. Almost sure invariance principle for sequential and nonstationary dynamical systems. Trans. Amer. Math. Soc., 369(8):5293-5316, 2017. doi:10.1090/tran/6812.[12] Christoph Kawan. Metric entropy of nonautonomous dynamical systems. Nonauton. Dyn. Syst., 1:26-52, 2014. doi:10. 2478/msds-2013-0003.[13] Christoph Kawan. Expanding and expansive time-dependent dynamics. Nonlinearity, 28(3):669-695, 2015. doi:10.1088/0951-7715/28/3/669.[14] Alexey Korepanov, Zemer Kosloff, and Ian Melbourne. Martingale-coboundary decomposition for families of dynamical systems. 2016. Preprint. arXiv:1608.01853.[15] Juho Leppänen and Mikko Stenlund. Quasistatic dynamics with intermittency. Math. Phys. Anal. Geom., 19(2):Art. 8, 23, 2016. URL: http://dx.doi.org/10.1007/s11040-016-9212-2.10.1007/s11040-016-9212-2[16] Juho Leppänen. Functional correlation decay and multivariate normal approximation for non-uniformly expanding maps. Nonlinearity, 30(11):4239, 2017. URL: http://stacks.iop.org/0951-7715/30/i=11/a=4239.[17] Carlangelo Liverani, Benoît Saussol, and Sandro Vaienti. A probabilistic approach to intermittency. Ergodic Theory Dynam. Systems, 19(3):671-685, 1999. URL: http://dx.doi.org/10.1017/S0143385799133856.10.1017/S0143385799133856[18] Anushaya Mohapatra andWilliam Ott. Memory loss for nonequilibriumopen dynamical systems. Discrete Contin. Dyn. Syst., 34(9):3747-3759, 2014. doi:10.3934/dcds.2014.34.3747.[19] Péter Nándori, Domokos Szász, and Tamás Varjú. A central limit theorem for time-dependent dynamical systems. J. Stat. Phys., 146(6):1213-1220, 2012. doi:10.1007/s10955-012-0451-8.[20] Matthew Nicol, Andrew Török, and Sandro Vaienti. Central limit theorems for sequential and random intermittent dynamical systems. 2016. To appear in Ergodic Theory and Dynamical Systems. doi:10.1017/etds.2016.69.[21] William Ott, Mikko Stenlund, and Lai-Sang Young. Memory loss for time-dependent dynamical systems. Math. Res. Lett., 16(3):463-475, 2009. doi:10.4310/MRL.2009.v16.n3.a7.[22] L. C. G. Rogers and David Williams. Diffusions, Markov processes, and martingales. Vol. 2. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 2000. Itô calculus, Reprint of the second (1994) edition. doi:10.1017/ CBO9781107590120.[23] Mikko Stenlund. A vector-valued almost sure invariance principle for Sinai billiards with random scatterers. Comm. Math. Phys., 325(3):879-916, 2014. doi:10.1007/s00220-013-1870-3.[24] Mikko Stenlund. An almost sure ergodic theorem for quasistatic dynamical systems. Math. Phys. Anal. Geom., 19(3):Art. 14, 18, 2016. doi:10.1007/s11040-016-9217-x.[25] Matteo Tanzi, Tiago Pereira, and Sebastian van Strien. Robustness of ergodic properties of nonautonomous piecewise expanding maps. 2016. Preprint. arXiv:1611.04016.

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Nonautonomous and Stochastic Dynamical Systemsde Gruyter

Published: Apr 3, 2018

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