Universal maps (maps whose renormalized iterations approximate every map in a given class) are locally generic in several spaces of diffeomorphisms [Bonatti--Díaz 2003, Turaev 2015]. In fluid dynamics, steady Euler flows whose Poincaré maps are universal are also known to be locally dense [Berger--Florio--PeraltaSalas, 2023]. Motivated by Arnold's vision [Arnold, 1966] that the complexity of orbits in celestial mechanics and that in fluids should be comparable, in the present paper we address the question of the existence of universal maps in celestial mechanics. We give a partial answer by proving a weak, finite-dimensional form of universal dynamics. More concretely, we show that every symplectic embedding of the disk into $\mathbb{R}^2$ can be approximated, with arbitrary precision, by a renormalization of a Poincaré map of a restricted planar circular $(n+1)$-body problem, for suitable $n$ and appropriate choice of the masses of the primaries. The proof relies on Gonchenko--Shilnikov--Turaev theory [Turaev 2003, Gonchenko--Turaev--Shilnikov 2007] and requires control of the dynamics near homoclinic tangencies of arbitrarily high order; the techniques developed in [Garrido--Martín--Paradela, 2025] are essential for such control.

Convective instabilities are studied from a Lagrangian perspective in order to gain new insights into how the resulting global, long-lived coherent flow structures organize themselves. We consider a 2D annular fluid layer uniformly heated from the inside and subject to radial gravity and propose several new Lagrangian diagnostics for characterizing its convective instabilities. In particular, we perform a comprehensive Lagrangian analysis of the flow field across a wide range of dimensionless parameters, establishing a heuristic correspondence between convective plumes and curves of local maxima of Finite-Time Lyapunov Exponent (FTLE) fields. Moreover, we characterize coherent swirling motions inside convective rolls, which are associated to the non-zero curvature of the flow. By introducing a sliding window method for our finite-time kinematic measures, we demonstrate a direct relationship with radial heat flux quantified by means of the Nusselt number and identify relevant dynamical transitions that leave a trace on both. Finally, we propose a formal criterion for determining viscous boundary layer (UBL) thickness by virtue of radial FTLE profiles and validated against a classical Eulerian method.