相关论文: Relative Chaos for $C_0$-Semigroups Beyond Topolog…
We construct a class of systems for which quantum dynamics can be expanded around a mean field approximation with essentially classical content. The modulus of the quantum overlap of mean field states naturally introduces a classical…
We study quantum chaos in $\textrm{T}\overline{\textrm{T}}$-deformed two-dimensional conformal field theories with gravitational anomaly and their holographic dual description in topologically massive gravity. Using pole-skipping and…
The work concentrates on relations, which are general and model independent in chaotic system, between time averages of a few (typically {\it very few}) observables. Equilibrium thermodynamics provides a guide and here is attempted to argue…
We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
For a commutative non-autonomous dynamical system we show that topological transitivity of the non-autonomous system induced on probability measures (hyperspaces) is equivalent to the weak mixing of the induced systems. Several counter…
This chapter gives an overview of transport problems where chaotic dynamics of the system plays a crucial role. We begin with single-particle transport problems and then come to conservative and then dissipative systems of identical…
The abstract hyperbolic sets are introduced. Continuous and differentiable mappings as well as rate of convergence and transversal manifolds are not under discussion, and the symbolic dynamics paradigm is realized in a new way. Our…
We generalize various notions of stability of invariant sets of dynamical systems to invariant measures, by defining a topology on the set of measures. The defined topology is similar, but not topologically equivalent to weak* topology, and…
Nature is intrinsically heterogeneous, and remarkable phenomena can only be observed in the presence of intrinsically nonlinear heterogeneities. Spontaneous pattern formation in nature has fascinated humankind for centuries, and the…
There is a long tradition of studying chaotic trajectories in systems whose integrability is broken by means of an external perturbation. Here we explore a different route to chaos, in the dynamics of extended bodies, which arises due to…
A theory of the novel spiral chaos state recently observed in Rayleigh-Benard convection is proposed in terms of the importance of invasive defects i.e defects that through their intrinsic dynamics expand to take over the system. The motion…
Many nonlinear dynamical systems exhibit symmetry, affording substantial benefits for control design, observer architecture, and data-driven control. While the classical notion of group invariance enables a cascade decomposition of the…
Randomization of the Lagrangian chaos in fluid dynamics has been analyzed using results of direct numerical simulations, laboratory measurements, and oceanic observations. The notion of distributed chaos has been used in order to quantify…
We introduce a new methodology for the analysis of the phenomenon of chaotic itinerancy in a dynamical system using the notion of entropy and a clustering algorithm. We determine systems likely to experience chaotic itinerancy by means of…
Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their…
In this article, I would like to express some of my views on the nature of turbulence. These views are mainly drawn from the author's recent results on chaos in partial differential equations \cite{Li04}. Fluid dynamicists believe that…
An algorithm to characterize collective motion is presented, with the introduction of ``collective Lyapunov exponent'', as the orbital instability at a macroscopic level. By applying the algorithm to a globally coupled map, existence of…
This article tackles a fundamental long-standing problem in quantum chaos, namely, whether quantum chaotic systems can exhibit sensitivity to initial conditions, in a form that directly generalizes the notion of classical chaos in phase…