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One of the common characteristics of chaotic maps or flows in high dimensions is "unstable dimensional variability", in which there are periodic points whose unstable manifolds have different dimensions. In this paper, in trying to…
The combination of photometry, spectroscopy and spectropolarimetry of the chemically peculiar stars often aims to study the complex physical phenomena such as stellar pulsation, chemical inhomogeneity, magnetic field and their interplay…
A suite of analytical and computational techniques based on symbolic representations of simple and complex dynamics, is further developed and employed to unravel the global organization of bi-parametric structures that underlie the…
We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…
Spherical Designs are finite sets of points on the sphere $\mathbb{S}^{d}$ with the property that the average of certain (low-degree) polynomials in these points coincides with the global average of the polynomial on $\mathbb{S}^{d}$. They…
Ordered chains (such as chains of amino acids) are ubiquitous in biological cells, and these chains perform specific functions contingent on the sequence of their components. Using the existence and general properties of such sequences as a…
One signature of an expanding universe is the time-variation of the cosmological abundances of its different components. For example, a radiation-dominated universe inevitably gives way to a matter-dominated universe, and critical moments…
Collective dynamics in proliferating anisotropic particle systems arise from an interplay between growth, division, and mechanical interactions, often mediated by particle shape. In classical models of prolate, rod-like growth, flow-induced…
Atherosclerosis is a chronic inflammatory disease occurs due to plaque accumulation in the inner artery wall. In atherosclerotic plaque formation monocytes and macrophages play a significant role in controlling the disease dynamics. In the…
Chaos as typical property of non-linear systems has revealed its crucial role in various problems of astrophysics and cosmology. The problems discussed at these lectures include planetary dynamics, galactic dynamics, reconstruction of the…
The spatiotemporal sculpturing of light beams with arbitrary phase and polarization topologies has garnered significant attention in recent years due to its potential to advance optical technologies and reveal novel physical phenomena.…
Various natural and engineered systems, from urban traffic flow to the human brain, can be described by large-scale networked dynamical systems. These systems are similar in being comprised of a large number of microscopic subsystems, each…
Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…
In biological systems, active agents such as actomyosin and cells move and interact on curved surfaces, exhibiting diverse phenomena. These observations have motivated studies of how curvature shapes their collective behavior. Here, using a…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
Building on work of Ruelle and Putnam in the Smale space case, Thomsen defined the homoclinic and heteroclinic $C^\ast$-algebras for an expansive dynamical system. In this paper we define a class of expansive dynamical systems, called…
Symmetries naturally occur in real-world networks and can significantly influence the observed dynamics. For instance, many synchronization patterns result from the underlying network symmetries, and high symmetries are known to increase…
Studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the distribution of particles at `microscales' to predict physical properties at `macroscales', whether for a liquid, composite material, or…
For a model system defined as combination of sequentially applied continuous transformations of a sphere, the question of arrangement of the parameter space around the domain of existence of the Plykin-type attractor is considered. Results…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…