On the non-randomness of modular arithmetic progressions: a solution to a problem by V. I. Arnold by Eda Cesaratto, Alain Plagne, Brigitte Vallée

“…We solve a problem by V. I. Arnold dealing with "how random" modular arithmetic progressions can be. …”
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Instability in Hamiltonian systems by A. Pumarino, Claudia Valls

“…The existence of this unlimited dynamical richness leads, in an unmistakable way, to the instability of the studied system. V. I. Arnold even discovered that, surprisingly, these situations often arise in a persistent way when an integrable Hamiltonian system is perturbed. …”
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Beltrami fields exhibit knots and chaos almost surely by Alberto Enciso, Daniel Peralta-Salas, Álvaro Romaniega

“…The motivation to consider this question, which arises in the study of stationary Euler flows in dimension 3, is V.I. Arnold’s 1965 speculation that a typical Beltrami field exhibits the same complexity as the restriction to an energy hypersurface of a generic Hamiltonian system with two degrees of freedom. …”
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Incidence coefficients in the Novikov Complex for Morse forms: rationality and exponential growth properties by Andrei Pajitnov

“…The incidence coefficients in the Novikov complex are obtained by counting the algebraic number of the trajectories of the gradient, joining the zeros of the Morse form. There is V.I.Arnold’s version of the exponential growth conjecture, which concerns the total number of trajectories. …”
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