动力系统

We show that any sequence of integers satisfying necessary Dold's congruences is realized as the sequence of fixed point indices of the iterates of an orientation-reversing homeomorphism of $\mathbb{R}^{m}$ for $m\geq 3$. As an element of…

Let $\Phi$ be a $C^\omega (\mathbb{C})$ self-conformal IFS on the plane, satisfying some mild non-linearity and irreducibility conditions. We prove a uniform spectral gap estimate for the transfer operator corresponding to the derivative…

The R\"ossler System is one of the best known chaotic dynamical systems, exhibiting a plethora of complex phenomena - and yet, only a few studies tackled its complexity analytically. In this paper we find sufficient conditions for the…

Consider the sequence of continued fraction convergents $p_n/q_n$ to a random irrational number. We study the distribution of the sequences $p_n \pmod{m}$ and $q_n \pmod{m}$ with a fixed modulus $m$, and more generally, the distribution of…

We explore the phase diagram for potentials in the space of H\"older continuous functions of a given exponent and for the dynamical system generated by a Pomeau--Manneville, or intermittent, map. There is always a phase where the unique…

We prove that for finitely generated free semigroup actions the average shadowing property, the weak asymptotic average shadowing property, the mean ergodic shadowing property, the almost asymptotic average shadowing property, the…

By a classical result of Kathleen Alligood and James Yorke we know that as we isotopically deform a map $f:ABCD\to\mathbb{R}^2$ to a Smale horseshoe map we should often expect the dynamical complexity to increase via a period--doubling…

Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number of solutions are discussed by means of a phase plane…

In this paper, we establish a connection between the spectral theory of the Koopman operator and the solution of the Hamilton Jacobi (HJ) equation. The HJ equation occupies a central place in systems theory, and its solution is of interest…

The bounded orbit conjecture says that every homeomorphism on the plane with each of its orbits being bounded must have a fixed point. Brouwer's translation theorem asserts that the conjecture is true for orientation preserving…

Several non-linear operators in stochastic analysis, such as solution maps to stochastic differential equations, depend on a temporal structure which is not leveraged by contemporary neural operators designed to approximate general maps…

For a family of dynamical systems with $k > 0$ independent first integrals evolving in a compact region of an Euclidean space, we study the equilibrium locus. We show that under mild and generic conditions, it is a smooth manifold that can…

Despite the huge efforts to develop and administer vaccines worldwide to cope with the COVID-19 pandemic, misinformation spreading through fake news in media and social networks about vaccination safety, make that people refuse to be…

We use a complex-valued transformation of the Kuramoto model to develop an operator-description of the linear stability in finite networks of nonlinear oscillators. This mathematical approach offers analytical predictions for the linear…

We study the behavior of probability measures under iteration of a surjective cellular automaton. We solve the following question in the negative: if the initial measure is ergodic and has full support, do all weak-* limit points of the…

We obtain estimates on the decay of correlations, Central Limit Theorem and Large Deviations for dynamical systems admitting an induced weak Gibbs--Markov map, for larger classes of observables with weaker regularity than H\"{o}lder,…

Understanding the emergence and stability of cooperation in public goods games is important due to its applications in fields such as biology, economics, and social science. However, a gap remains in comprehending how mutations, both…

Non-local continuity equation describes an infinite system of identical particles, which interact with each other through the common field. Solution of this equation is a probability measure that stands for spatial distribution of…

In this paper we study some basic problems about Toeplitz subshifts of finite topological rank. We define the notion of a strong Toeplitz subshift of finite rank $K$ by combining the characterizations of Toeplitz-ness and of finite…

Let $G$ be a discrete countable infinite group. Let $T$ and $\widetilde T$ be two rank-one $\sigma$-finite measure preserving actions of $G$ and let $\mathcal T$ and $\widetilde {\mathcal T}$ be the cutting-and-stacking parameters that…