Related papers: On the fixed points set of differential systems re…
We prove that measure-preserving symmetries of an $n$-dimensional differential system preserve its divergence and the divergence derivatives along the solutions. Also, we prove that measure-preserving reversibilities preserve odd-order…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
In reversible dynamical systems, it is frequently of importance to understand symmetric features. The aim of this paper is to explore symmetric periodic points of reversible maps on planar domains invariant under a reflection. We extend…
An invertible dynamical system with some hyperbolic structure is considered. Upper estimates for the correlations of continuous observables is given in terms of modulus of continuity. The result is applied to certain H\'enon maps and…
Non-minimal gauge models with exact unbroken improper space-time symmetries are constructed and their cosmological and astrophysical implications explored.
We give a natural notion of nondegeneracy for singular points of integrable non-Hamiltonian systems, and show that such nondegenerate singularities are locally geometrically linearizable and deformation rigid in the analytic case. We…
Circumventing the reciprocity invariance has posed an interesting challenge in the design of modern devices for wave engineering. In passive devices, operating the device in the nonlinear response regime is a common means for realizing…
We prove that for every planar differential system with a period annulus there exists an involution $\sigma$ such that the system is $\sigma$-symmetric. We also prove that for for every planar differential system with a period annulus there…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
We establish a structure theorem for the integral points on moduli of special linear rank two local systems over surfaces, using mapping class group descent and boundedness results for systoles of local systems.
Robustness guarantees are important properties to be looked for during control design. They ensure stability of closed-loop systems in face of uncertainties, unmodeled effects and bounded disturbances. While the theory on robust stability…
We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
Stability of the zero solution plays an important role in the investigation of positive systems. In this note, we revisit the $\mu$-stability of positive nonlinear systems with unbounded time-varying delays. The system is modelled by…
The applicability of time-reversal symmetry to nonlinear optics is discussed, both from macroscopic (Maxwell equations) and microscopic (quantum theoretical) point of view. We find that only spatial operations can be applied for the…
In this paper we study Chaplygin's Reducibility Theorem and extend its applicability to nonholonomic systems with symmetry described by the Hamilton-Poincare-d'Alembert equations in arbitrary degrees of freedom. As special cases we extract…
We present a local almost everywhere regularity result for a general nonlinear non-diagonal parabolic system, which main part depends on symmetric part of the gradient.
The absence of time-reversal symmetry is a fundamental property of many nonlinear time series. Here, we propose a new set of statistical tests for time series irreversibility based on standard and horizontal visibility graphs. Specifically,…
We deal with germs of diffeomorphisms that are reversible under an involution. We establish that this condition implies that, in general, both the family of reversing symmetries and the group of symmetries are not finite, in contrast with…