Related papers: Emergent transfinite topological dynamics
The research in topological materials and meta-materials reached maturity and is now gradually entering the phase of practical applications and devices. However, scaling down the experimental demonstrations definitely presents a challenge.…
The topological snail is a geometric universal plane object, described by matrices in the projective special linear group with integer coefficients. It has many nice properties : in the case of three points, it natually defines a…
Dynamical fluctuations or rare events associated with atypical trajectories in chaotic maps due to specific initial conditions can crucially determine their fate, as the may lead to stability islands or regions in phase space otherwise…
The goal of this article is to study how combinatorial equivalence implies topological conjugacy. For that, we introduce the concept of kneading sequences for nonautonomous discrete dynamical systems and show that these sequences are a…
Encouraged by the AdS/CFT correspondence, we study emergent local geometry in large N multi-matrix models from the perspective of a strong coupling expansion. By considering various solvable interacting models we show how the emergence or…
For any dynamical system $T:X\rightarrow X$ of a compact metric space $X$ with $g-$almost product property and uniform separation property, under the assumptions that the periodic points are dense in $X$ and the periodic measures are dense…
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
We study the dynamics of the exponential maps $E_{\lambda}: \mathbb{C} \longrightarrow \mathbb{C}$ defined by $E_{\lambda}(z) = \lambda e^z$, where $\lambda > \frac{1}{e}$. We prove that for itineraries of a certain form, the set of all…
The stable functionality of networked systems is a hallmark of their natural ability to coordinate between their multiple interacting components. Yet, strikingly, real-world networks seem random and highly irregular, apparently lacking any…
Dynamical compactness with respect to a family as a new concept of chaoticity of a dynamical system was introduced and discussed in [22]. In this paper we continue to investigate this notion. In particular, we prove that all dynamical…
We study independent and identically distributed random iterations of continuous maps defined on a connected closed subset $S$ of the Euclidean space $\mathbb{R}^{k}$. We assume the maps are monotone (with respect to a suitable partial…
We investigate the iterative behaviour of continuous order preserving subhomogeneous maps that map a polyhedral cone into itself. For these maps we show that every bounded orbit converges to a periodic orbit and, moreover, that there exists…
We quantify the asymptotic behaviour of multidimensional drifltess diffusions in domains unbounded in a single direction, with asymptotically normal reflections from the boundary. We identify the critical growth/contraction rates of the…
The last years have witnessed rapid progress in the topological characterization of out-of-equilibrium systems. We report on robust signatures of a new type of topology -- the Euler class -- in such a dynamical setting. The enigmatic…
In this paper we study topological entropy and recurrence properties of non-autonomous dynamical system generated by a family of continuous self maps on a compact space X. Specially, we introduce the pseudo-entropy and…
We introduce the construction of a new framework for probing discrete emergent geometry and boundary-boundary observables based on a fundamentally a-dimensional underlying network structure. Using a gravitationally motivated action with…
Systems whose organization displays causal asymmetry constraints, from evolutionary trees to river basins or transport networks, can be often described in terms of directed paths (causal flows) on a discrete state space. Such a set of paths…
We revisit the equilibrium one-dimensional $\phi^4$ model from the dynamical systems point of view. We find an infinite number of periodic orbits which are computationally stable. At the same time some of the orbits are found to exhibit…
In their earlier work (Ergodic Th. Dynam. Sys., 34: 1699 -1723, 10 2014), the authors introduced the so called F-aperiodic orbits of a dynamical system on a compact metric space X, which satisfy a quantitative condition measuring its…
In the first half of the paper, some recent advances in coupled dynamical systems, in particular, a globally coupled map are surveyed. First, dominance of Milnor attractors in partially ordered phase is demonstrated. Second, chaotic…