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The star transform is a generalized Radon transform mapping a function of two variables to its integrals along "star-shaped" trajectories, which consist of a finite number of rays emanating from a common vertex. Such operators appear in…
Quasi-invariant measures for non-discrete groups of diffeomorphisms containing a Morse-Smale dynamics are studied. The assumption concerning the presence of a Morse-Smale dynamics allows us to extend to higher dimensions a number of…
The P-matrix approach for the determination of the orbit spaces of compact linear groups enabled to determine all orbit spaces of compact coregular linear groups with up to 4 basic polynomial invariants and, more recently, all orbit spaces…
We analyze maximum entropy random graph ensembles with constrained degrees, drawn from arbitrary degree distributions, and a tuneable number of 3-loops (triangles). We find that such ensembles generally exhibit two transitions, a clustering…
Conjugations in space $L^2$ of the unit circle commuting with multiplication by $z$ or intertwining multiplications by $z$ and $\bar z$ are characterized. We also study their behaviour with respect to the Hardy space, subspaces invariant…
We study dynamical systems acting on the path space of a stationary (non-simple) Bratteli diagram. For such systems we explicitly describe all ergodic probability measures invariant with respect to the tail equivalence relation (or the…
Polynomial invariants of a group action often appear only in high degree, and in many representations the invariant ring imposes severe degree constraints before any nontrivial invariants can occur. In contrast, the larger class of unitary…
We started from computer experiments with simple one-dimensional ergodic dynamical systems called interval exchange transformations. Correlators in these systems decay as a power of time. In the simplest non-trivial case the exponent is…
Topological quantum phase transitions are characterised by changes in global topological invariants. These invariants classify many body systems beyond the conventional paradigm of local order parameters describing spontaneous symmetry…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
Studying the orbital stability of multi-planet systems is essential to understand planet formation, estimate the stable time of an observed planetary system, and advance population synthesis models. Although previous studies have primarily…
For an integer $m \geq 2$, let $\mathcal{P}_m$ be the partition of the unit interval $I$ into $m$ equal subintervals, and let $\mathcal{F}_m$ be the class of piecewise linear maps on $I$ with constant slope $\pm m$ on each element of…
We show that Sarnak's conjecture on Mobius disjointness holds for interval exchange transformations on three intervals (3-IETs) that satisfy a mild diophantine condition.
The iron-based superconductors allow for a zoo of possible order parameters due to their orbital degrees of freedom. These order parameters are often written in an orbital basis, as this allows to distinguish their different symmetry.…
The mutual compatibility of the dynamical equations and constraints describing a massive particle of arbitrary spin, though essential for consistency, is generically lost in the presence of interactions. The conventional Lagrangian approach…
We describe the invariant metrics on real flag manifolds and classify those with the following property: every geodesic is the orbit of a one-parameter subgroup. Such a metric is called g.o. (geodesic orbit). In contrast to the complex…
Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed "cutting and shuffling" of a line segment), and we present a comprehensive…
This paper describes magnetospheric waves of very long wavelength in thin magnetic filaments. We consider an average magnetospheric configuration with zero ionospheric conductance and calculate waves using two different formulations:…
The two-photon-exchange diagrams for atoms with single valence electrons are investigated. Calculation formulas are derived for an arbitrary state within the rigorous bound-state QED framework utilizing the redefined vacuum formalism. In…
The topological classification of the inner mappings on the fully invariant regular components of the wandering set with a special attracting boundary up to the topological conjugacy is defined in terms of distinguishing graph. Two inner…