My main research interest is Rigorous Computational Methods for Ergodic Theory: using computer-aided estimates to prove results on the statistical properties of dynamical systems and stochastic processes.
Certified spectral approximation of transfer operators and the Gauss map (2026) I. Nisoli arXiv:2602.19435
A pseudospectral approach to rigorous numerical estimation of Ruelle resonances of transfer operators (2025) A. Blumenthal, I. Nisoli, T. Taylor-Crush arXiv:2507.09021
Efficient computation of stationary measures and the Lyapunov landscape for families of random dynamical systems with smooth additive noise (2025) S. Galatolo, C. Lopez Vereau, L. Marangio, I. Nisoli arXiv:2508.03895
Designing robust trajectories by lobe dynamics in low-dimensional Hamiltonian systems (2024) N. Hiraiwa, M. Bando, Y. Sato, I. Nisoli Physical Review Research 6, L022046 arXiv:2404.00721
Rigorous computation of linear response for intermittent maps (2023) I. Nisoli, T. Taylor-Crush Journal of Statistical Physics 190, 192 arXiv:2201.03923 | PDF
A general framework for the rigorous computation of invariant densities and the coarse-fine strategy (2023) S. Galatolo, M. Monge, I. Nisoli, F. Poloni Chaos, Solitons & Fractals 170, 113329 arXiv:2212.05017 | PDF
How does noise induce order? (2023) I. Nisoli Journal of Statistical Physics 190, 22 arXiv:2003.08422 | PDF
Noise induced order for skew-products over a non-uniformly expanding base (2022) A. Blumenthal, I. Nisoli Nonlinearity 35(10) arXiv:2109.12183 | PDF
Existence of multiple noise-induced transitions in Lasota–Mackey maps (2021) T. Chihara, S. Galatolo, I. Nisoli, Y. Sato Chaos 32(1), 013117 PDF
Existence of noise induced order, a computer aided proof (2020) S. Galatolo, M. Monge, I. Nisoli Nonlinearity 33(9), 4237–4276 arXiv:1702.07024 | PDF
A rigorous computational approach to linear response (2018) W. Bahsoun, S. Galatolo, I. Nisoli, X. Niu Nonlinearity arXiv:1506.08661 | PDF
Decay of correlations, quantitative recurrence and logarithm law for contracting Lorenz attractors (2018) S. Galatolo, I. Nisoli, M. J. Pacifico Journal of Statistical Physics arXiv:1701.08743 | PDF
Rigorous approximation of stationary measures and convergence to equilibrium for iterated function systems (2016) S. Galatolo, M. Monge, I. Nisoli Journal of Physics A: Mathematical and Theoretical PDF
Rigorous approximation of diffusion coefficients for expanding maps (2016) W. Bahsoun, S. Galatolo, I. Nisoli, X. Niu Journal of Statistical Physics PDF
Rigorous computation of invariant measures and fractal dimension for maps with contracting fibers: 2D Lorenz-like maps (2015) S. Galatolo, I. Nisoli Ergodic Theory and Dynamical Systems arXiv:1402.5918 | PDF
An elementary way to rigorously estimate convergence to equilibrium and escape rates (2015) S. Galatolo, I. Nisoli, B. Saussol Journal of Computational Dynamics arXiv:1404.7113 | PDF
Towards a Morse theory on Banach spaces via ultrafunctions (2015) V. Benci, I. Nisoli Arab Journal of Mathematical Sciences PDF
An elementary approach to rigorous approximation of invariant measures (2014) S. Galatolo, I. Nisoli SIAM Journal on Applied Dynamical Systems arXiv:1109.2342 | PDF
Probability, statistics and computation in dynamical systems (2014) S. Galatolo, I. Nisoli, C. Rojas Mathematical Structures in Computer Science PDF
Partial holomorphic connections and extension of foliations (2012) I. Nisoli Kyoto Journal of Mathematics 52(3), 517–555 arXiv:1010.3450 | PDF
Shrinking targets in fast mixing flows and the geodesic flow on negatively curved manifolds (2011) S. Galatolo, I. Nisoli Nonlinearity arXiv:1101.0486 | PDF