The algebra of symmetries of a quantum resonance oscillator in the case of three and more frequencies is described using a finite (minimal) basis of generators and polynomial relations. For this algebra, we construct quantum leaves with complex structure (an analog of classical symplectic leaves) and a quantum K¨ahlerian 2-form, a reproducing measure, as well as the corresponding irreducible representations and coherent states.
We consider the problem of potential interaction between a finite-dimensional linear Lagrangian system and an infinite-dimensional one (a system of linear oscillators and a thermostat). We study the final dynamics of the system. Under natural assumptions, this dynamics turns out to be very simple and admits an explicit description because the thermostat produces an effective dissipation despite the energy conservation and the Lagrangian nature of the system. We use the methods of , where the final dynamics of the finite-dimensional subsystem is studied in the case when it has one degree of freedom and a linear potential or (under additional assumptions) polynomial potential. We consider the case of finite-dimensional subsystems with arbitrarily many degrees of freedom and a linear potential and study the final dynamics of the system of oscillators and the thermostat. The necessary assertions from  are given with proofs adapted to the present situation.
 D. Treschev, “Oscillator and thermostat”, Discrete Contin. Dyn. Syst. 28:4 (2010), 1693–1712
This paper is devoted to problems on equivariant embeddings of quasi-toric manifolds in Euclidean and projective spaces. We construct explicit embeddings and give bounds for the dimensions of the embeddings in terms of combinatorial data that determine such manifolds. We show how familiar results on complex projective varieties in toric geometry can be obtained under additional restrictions on the combinatorial data.
We classify smooth Fano threefolds with infinite automorphism groups.
This is the first paper in a series of two presenting a digest of the proof of the finiteness theorem for limit cycles of a planar polynomial vector field. At the same time we sketch the proof of the following two theorems: an analogous result for analytic vector fields, and a description of the asymptotics of the monodromy transformation for polycycles of such fields. © 2016 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.
In the third paper of the series we complete the proof of our main result: a description of the ergodic decomposition of infinite Pickrell measures. We first prove that the scaling limit of the determinantal measures corresponding to the radial parts of Pickrell measures is precisely the infinite Bessel process introduced in the first paper of the series. We prove that the ‘Gaussian parameter’ for ergodic components vanishes almost surely. To do this, we associate a finite measure with each configuration and establish convergence to the scaling limit in the space of finite measures on the space of finite measures. We finally prove that the Pickrell measures corresponding to different values of the parameter are mutually singular.
We present a study of real Hurwitz numbers enumerating a special kind of real meromorphic functions, which we call simple framed purely real functions. We deduce partial differential equations of cut-and-join type for generating functions for these numbers. We also construct a topological field theory for them.
We study Fano threefolds with terminal Gorenstein singularities admitting a ‘minimal’ action of a finite group. We prove that under certain additional assumptions such a variety contains no planes. We also obtain upper bounds for the number of singular points of certain Fano threefolds with terminal factorial singularities.
We considerone-parameter families (general unfoldings)of two- dimensional reversible diffeomorphisms that contain a diffeomorphism with a symmetric non-transversal heteroclinic cycle. We show that in such families there exist Newhouse intervals of parameters such that the values corresponding to the co-existence of infinitely many stable, completely unstable, saddle and symmetric elliptic periodic orbits are generic (that is, they form Baire second-category sets). Also, the closures of the sets of orbits of different types have non-empty intersections.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators in these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We introduce the notions of consistent pairs and consistent chains of $ t$-structures and prove that two consistent chains of $ t$-structures generate a distributive lattice. The technique developed is then applied to the pairs of chains obtained from the standard $ t$-structure on the derived category of coherent sheaves and the dual $ t$-structure by means of the shift functor. This yields a family of $ t$-structures whose hearts are known as perverse coherent sheaves. Access this article Login options Individual login Institutional loginvia Athens/Shibboleth The computer you are using is not registered by an institution with a subscription to this article. Please log in below. Find out more about journal subscriptions at your site. Purchase this article online Buy this article £33.00 (£39.60 incl. VAT) $59.70 US Dollar price There are no additional delivery charges. By purchasing this article, you are accepting IOP's Terms and Conditions for Document Delivery. If you would like to buy this article, but not online, please contact firstname.lastname@example.org. Make a recommendation To gain access to this content, please complete the Recommendation Form and we will follow up with your librarian or Institution on your behalf. For corporate researchers we can also follow up directly with your R&D manager, or the information management contact at your company. Recommend this journal Institutional subscribers have access to the current volume, plus a 10-year back file (where available). Subscribe to this journal The title that you are trying to access is not part of the IOP Historic Archive. You can purchase a copy of the article that you wish to view. Related Articles Hyperplane sections and derived categories Derived categories of coherent sheaves and equivalences between them PROJECTIVE BUNDLES, MONOIDAL TRANSFORMATIONS, AND DERIVED CATEGORIES OF COHERENT SHEAVES More Related Review Articles Classification of isomonodromy problems on elliptic curves Number-theoretic properties of hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves over the rational number field Geometric structures on moment-angle manifolds More
We study elements $\tau$ of order two in the birational automorphism groups of rationally connected three-dimensional algebraic varieties such that there exists a non-uniruled divisorial component of the $\tau$-fixed point locus. Using the equivariant minimal model program, we give a rough classification of such elements.
We show that the only sporadic simple group such that some of its faithful representations or some faithful representations of its stem extensions give rise to exceptional (weakly-exceptional but not exceptional, respectively) quotient singularities is the Hall–Janko group (the Suzuki group, respectively).