Submitted Preprints:

  • Bedrossian, Jacob; Blumenthal, Alex; Punshon-Smith, Samuel, 2020. "A regularity method for lower bounds on the Lyapunov exponent for stochastic differential equations." arXiv preprint arXiv:  2007.15827. Submitted. [arxiv]
  • Blumenthal, Alex; Xue, Jinxin; Yang, Yun, 2020. "Lyapunov exponents for random perturbations of coupled standard maps." arXiv preprint arXiv: 2004.10626. Submitted. [arxiv]
  • Bedrossian, Jacob; Blumenthal, Alex; Punshon-Smith, Samuel, 2019. "The Batchelor spectrum of passive scalar turbulence in stochastic fluid mechanics." arXiv preprint arXiv: 1911.11014. Submitted. [arxiv]
  • Bedrossian, Jacob; Blumenthal, Alex; Punshon-Smith, Samuel, 2019. " Almost-sure enhanced dissipation and uniform-in-diffusivity exponential mixing for advection-diffusion by stochastic Navier-Stokes." arXiv preprint arXiv:  1911.01561. Submitted. [arxiv]
  • Bedrossian, Jacob; Blumenthal, Alex; Punshon-Smith, Samuel, 2019. "Almost-sure exponential mixing of passive scalars by the stochastic Navier-Stokes equations." arXiv preprint arXiv: 1905.03869. Submitted. [arxiv]
  • Bedrossian, Jacob; Blumenthal, Alex; Punshon-Smith, Samuel, 2018. "Lagrangian chaos and scalar advection in stochastic fluid mechanics." arXiv preprint arXiv: 1809.06484. Submitted. [arxiv]
  • Blumenthal, Alex and Yang, Yun, 2018. "Positive Lyapunov exponent for random perturbations of predominantly expanding multimodal circle maps." arXiv preprint arXiv:1805.09219. Submitted. [arxiv]

Accepted or Published Papers:

  • Blumenthal, Alex; De Simoi, Jacopo; and Zhang, Ke, 2018. "Diffusion limit for a slow-fast standard map," accepted to CMP. [arxiv]
  • Blumenthal, Alex and Young, Lai-Sang (2019). Equivalence of physical and SRB measures in random dynamical systems. Nonlinearity, 32(4), 1494. [arxiv]
  • Blumenthal, Alex, 2017. "Statistical properties for compositions of standard maps with increasing coefficent," accepted to ETDS (2019) [arxiv]
  • Blumenthal, Alex; Xue, Jinxin; and Young, Lai-Sang, (2018). "Lyapunov exponents and correlation decay for random perturbations of some prototypical 2d maps." Communications in Mathematical Physics, 359(1), pp.347-373. [doi]
  • Blumenthal, Alex, & Latushkin, Yuri. (2019). The Selgrade decomposition for linear semiflows on Banach spaces. Journal of Dynamics and Differential Equations, 31(3), pp.1427-1456. [arxiv]
  • Blumenthal, Alex and Young, Lai-Sang. Absolute continuity of stable foliations for mappings of Banach spaces. Communications in Mathematical Physics, 354(2), pp.591-619 (2017). [arxiv]
  • Blumenthal, Alex; Xue, Jinxin; and Young, Lai-Sang. “Lyapunov exponents for random perturbations of some area-preserving maps including the Standard map,” Annals of Mathematics 185 (1), pp.285-310 (2017). [arxiv]
  • Blumenthal, Alex and Morris, Ian D. "Characterization of dominated splittings for operator cocycles acting on Banach spaces." To appear in Journal of Differential Equations. (2019) [arxiv]
  • Blumenthal, Alex and Young, Lai-Sang, 2017. Entropy, volume growth and SRB measures for Banach space mappings. Inventiones mathematicae, 207(2), pp.833-893. [arxiv]
  • Blumenthal, Alex. "A volume-based approach to the multiplicative ergodic theorem on Banach spaces,” Discrete and Continuous Dynamical Systems A 36 (5) 2377-2403 (2016). [arxiv] 
    • Note: There is an error in Lemma 3.8. An erratum has been submitted.
  • Blumenthal, Alex and Fernandez, Bastien. “Asymptotic periodicity in networks of degrade-and-fire oscillators,” Physica D 323-324, 49-56 (2015). [arxiv]
  • Blumenthal, Alex and Fernandez, Bastien. "Population Dynamics of Globally Coupled Degrade-and-Fire Oscillators." Journal of Dynamics and Differential Equations (2014). doi:10.1007/s10884-015-9449-7 [arxiv]

Thesis:

Blumenthal, Alex, 2016. Nonuniformly hyperbolic theory for Banach space mappings (Doctoral dissertation, New York University).