Related papers: Dynamical properties of families of holomorphic ma…
We study dynamical properties of the Fibonacci trace map - a polynomial map that is related to numerous problems in geometry, algebra, analysis, mathematical physics, and number theory. Persistent homoclinic tangencies, stochastic sea of…
Continuum hydrodynamic models of active liquid crystals have been used to describe dynamic self-organising systems such as bacterial swarms and cytoskeletal gels. A key prediction of such models is the existence of self-stabilising kink…
We study ergodic properties of compositions of holomorphic endomorphisms of the complex projective space chosen independently at random according to some probability distribution. Along the way, we construct positive closed currents which…
Flexible mechanical metamaterials are compliant structures engineered to achieve unique properties via the large deformation of their components. While their static character has been studied extensively, the study of their dynamic…
In this paper, we give a precise meaning to the following fact, and we prove it: $C^1$-open and densely, all the non-hyperbolic ergodic measures generated by a robust cycle are approximated by periodic measures. We apply our technique to…
Relationships between a chaotic behavior and closely related properties of topological transitivity, sensitivity to initial conditions, density of closed orbits of homeomorphism groups and their countable products are investigated. We…
We prove that every bounded strictly $J$-convex region equipped with the Kobayashi metric is hyperbolic in the sense of Gromov. We apply this result to the study of the dynamics of pseudo-holomorphic maps.
Skew pentagram maps act on polygons by intersecting diagonals of different lengths. They were introduced by Khesin-Soloviev in 2015 as conjecturally non-integrable generalizations of the pentagram map, a well-known integrable system. In…
We construct examples illustrating that dynamically-defined distributions of holomorphic diffeomorphisms on compact complex manifolds are not necessarily holomorphic in any open subset. More precisely, for any $n\geq 5$, we construct a…
We perform molecular dynamics simulations to characterize the occurrence of inhomogeneous shear flows in soft jammed materials. We use rough walls to impose a simple shear flow and study the athermal motion of jammed assemblies of soft…
We consider a non-autonomous dynamical system formed by coupling two piecewise-smooth systems in $\RR^2$ through a non-autonomous periodic perturbation. We study the dynamics around one of the heteroclinic orbits of one of the…
In this article, we develop a functional-analytic framework to establish existence, uniqueness, regularity of disintegration, and statistical properties of equilibrium states for a broad class of dynamical systems, potentially discontinuous…
We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic…
We study the specification property for partially hyperbolic dynamical systems. In particular, we show that if a partially hyperbolic diffeomorphism has two saddles with different indices, and stable manifold of one of them coincides with…
In this paper, we investigate some dynamical properties near a nonhyperbolic fixed point. Under some conditions on the higher nonlinear terms, we establish a stable manifold theorem and a degenerate Hartman theorem. Furthermore, the finite…
We study the dynamics of meromorphic maps for a compact Kaehler manifold X. More precisely, we give a simple criterion that allows us to produce a measure of maximal entropy. We can apply this result to bound the Lyapunov exponents. Then,…
We study the dynamic structure factor of fluctuating elastic thin sheets subject to conservative (athermal) random forcing. In Steinbock, Katzav & Boudaoud, Phys. Rev. Research 4, 033096 (2022), the static structure factor of such a sheet…
We uncover a geometric organization of the differential equations for the wavefunction coefficients of conformally coupled scalars in power-law cosmologies. To do this, we introduce a basis of functions inspired by a decomposition of the…
Exploiting the "natural" frame of space curves, we formulate an intrinsic dynamics of twisted elastic filaments in viscous fluids. A pair of coupled nonlinear equations describing the temporal evolution of the filament's complex curvature…
Aspects of the Nos\'e and Nos\'e-Hoover dynamics developed in 1983-1984 along with Dettmann's closely related dynamics of 1996, are considered. We emphasize paradoxes associated with Liouville's Theorem. Our account is pedagogical, focused…