Related papers: Mean field coupled dynamical systems: Bifurcations…
We investigate the monitored dynamics of many-body quantum systems in which projective measurements of extensive operators are alternated with unitary evolution. Focusing on mean-field models characterized by all-to-all interactions, we…
Metric mean dimension is a geometric invariant of dynamical systems with infinite topological entropy. We relate this concept with the fractal structure of the phase space and the H\"older regularity of the map. Afterwards we improve our…
We explore the influence of dissipation on a paradigmatic driven-dissipative model where a collection of two level atoms interact with both quadratures of a quantum cavity mode. The closed system exhibits multiple phase transitions…
General covariance is a crucial notion in the study of field theories in curved spacetime. A field theory defined with respect to a semi-Riemannian metric is generally covariant if two metrics which are related by a diffeomorphism produce…
For non-monotone single and two-populations time-dependent Mean-Field Game systems we obtain the existence of an infinite number of branches of non-trivial solutions. These non-trivial solutions are in particular shown to exhibit an…
This paper deals with random perturbations of diffeomorphisms on n-dimensional Riemannian manifolds with distributions supported on k-dimensional disks, where k<n. First we demonstrate general but not very intuitive conditions which…
Recent work has introduced the concept of finite-time scaling to characterize bifurcation diagrams at finite times in deterministic discrete dynamical systems, drawing an analogy with finite-size scaling used to study critical behavior in…
We consider an independently identically distributed random dynamical system generated by finitely many, non-uniformly expanding Markov interval maps with a finite number of branches. Assuming a topologically mixing condition and the…
We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…
A pitchfork bifurcation of an $(m-1)$-dimensional invariant submanifold of a dynamical system in $\mathbb{R}^m$ is defined analogous to that in $\mathbb{R}$. Sufficient conditions for such a bifurcation to occur are stated and existence of…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
We generalize the observable diameter and the separation distance for metric measure spaces to those for pyramids, and prove some limit formulas for these invariants for a convergent sequence of pyramids. We obtain various applications of…
In this paper we describe physical properties arising in the vicinity of two coupled quantum phase transitions. We consider a phenomenological model based on two scalar order parameter fields locally coupled biquadratically and having a…
The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables,…
We introduce a new method for determining the global stability of synchronization in systems of coupled identical maps. The method is based on the study of invariant measures. Besides the simplest non-trivial example, namely two…
Systems of a large number N of globally coupled maps have become popular as a relatively simple prototype of high-dimensional dynamics, showing many interesting and typical phenomena like synchronisation, cluster formation and…
It is known that the asymptotic invariant manifolds around an unstable periodic orbit in conservative systems can be represented by convergent series (Cherry 1926, Moser 1956, 1958, Giorgilli 2001). The unstable and stable manifolds…
An overview of recent advances in the theory of critical phenomena in $d$-dimensional weakly anisotropic systems is given. On the basis of a generalized shear transformation between anisotropic and isotropic systems, exact and approximate…
The field-theoretical model describing multicritical phenomena with two coupled order parameters with n_{||} and n_{\perp} components and of O(n_{||}) \oplus O(n_{\perp}) symmetry is considered. Conditions for realization of different types…
Many natural and technological systems fail to adapt to changing external conditions and move to a different state if the conditions vary too fast. Such "non-adiabatic" processes are ubiquitous, but little understood. We identify these…