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Important information about the dynamical structure of a differential system can be revealed by looking into its invariant compact manifolds, such as equilibria, periodic orbits, and invariant tori. This knowledge is significantly increased…

As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…

Spatiotemporally chaotic dynamics of a Kuramoto-Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as…

We formalize a minimal setting in which a chronology (a strict partial order on events) is forced by consistency of distributed information under local composability. The system maintains distributed records interpreted as constraints over…

The discrete complex Ginzburg-Landau equation is a fundamental model for the dynamics of nonlinear lattices incorporating competitive dissipation and energy gain effects. Such mechanisms are of particular importance for the study of…

The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to…

In problems where the temporal evolution of a nonlinear system cannot be followed, a method for studying the fluctuations of spatial patterns has been developed. That method is applied to well-known problems in deterministic chaos (the…

We discover that the energy-integral of time-delay is an adiabatic invariant in quantum scattering theory and corresponds classically to the phase space volume. The integral thus found provides a quantization condition for resonances,…

Impulsive dynamical systems, modeled by a continuous semiflow and an impulse function, may be discontinuous and may have non-intuitive topological properties, as the non-invariance of the non-wandering set or the non-existence of invariant…

Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of…

We analyze the stability of general nonlinear discrete-time stochastic systems controlled by optimal inputs that minimize an infinite-horizon discounted cost. Under a novel stochastic formulation of cost-controllability and detectability…

We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate…

This study analyzes the Collatz map through nonlinear dynamics. By embedding integers in Sharkovsky's ordering, we show that odd initial values suffice for full dynamical characterization. We introduce ``direction phases'' to partition…

Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…

Constructal Law states that a finite-size flow system that persists in time evolves its configuration so as to provide progressively easier access to the currents that flow through it. Classical Constructal theory derives hierarchical flow…

The theory of stationary spatially localized patterns in dissipative systems driven by time-independent forcing is well developed. With time-periodic forcing related but time-dependent structures may result. These may consist of breathing…

A one-dimensional dynamical system with a marginal quasiperiodic gradient is presented as a mathematical extension of a nonuniform oscillator. The system exhibits a nonchaotic stagnant motion, which is reminiscent of intermittent chaos. In…

We use the Liouville-von Neumann (LvN) approach to study the dynamics and the adiabaticity of a time-dependent driven anharmonic oscillator as an eample of non-equilibrium quantum dynamics. We show that the adiabaticity is minimally broken…

The notion of integrability is discussed for classical nonautonomous systems with one degree of freedom. The analysis is focused on models which are linearly spanned by finite Lie algebras. By constructing the autonomous extension of the…

Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by…