Petersburg State University (St. Petersburg); Starilov Yu.N., D.Sc.(Law), Prof., Voronezh State University (Voronezh); Strongin R.G., D.Sc.(Physics & Mathematics), Prof., UNN; Surikov I.E., D.Sc.(History), Prof., RAS. Member of the Russian Academy of Sciences, RAS Institute of World History (Moscow);. Political Science), Prof., University of San Francisco (San Francisco, USA); Shirinyants A.A., D.Sc.(Political Science), Prof., Lomonosov Moscow State University (Moscow).
The Concept of Integrability for Multifunctions and Dynamics of the Trace Map
In this study, we investigate the influence of chaotic behavior in complex networks by changing network topology. Let a skewed product F ∈Tf b3(In) satisfy the following conditions:. Y.1) the map f1 is totally topologically transitive;.
Then a tilted product F is fully transitive and has a dense set of periodic points in the phase space In.
Almost- and near-solutions of equations in unitary matrices
A system of equations W is said to be unitarily testable if for any >0 there exists δ >0 such that any unitary δ-near solution to W is a -near solution to W . Using the techniques of D.Kazhdan and A.Zuk we give a sufficient condition to the group to be unit testable.
Three types of dynamical chaos
Here N(X) is the normal subgroup of F generated by X.) Then W is unitarily testable if and only if W is. Thus, in light of the above statement one can speak of unit testable finite presented groups.
Characteristics of networks with hyperbolic geometry and symbolic dynamics
In Proceedings of the 10th Mediterranean Conference on Control and Automation (MED 2002), Lisbon, Portugal, July 2002.
On topology of manifolds admitting Morse-Smale systems without intersections of codimension one separatrices
On Embedding of Morse–Smale Diffeomorphisms in Topological Flows
Superposition principle for the continuity equation in a bounded domain
In this work, we propose an analogue of the Superposition Principle for the continuity equation in a bounded domain Ω⊂Rd. Our results are based on the structure of normal 1 currents (or charges), described by Smirnov [4] and later by Paolini and Stepanov [5, 6].
On basic sets of Smale-Vietoris A-diffeomorphisms
Networks of pulse delay coupled oscillators: reduction to discrete maps
Some properties of singular hyperbolic and Lorenz-type attractors
The circle map is a one-dimensional discrete-time map and exhibits different types of behavior as the function parameters change. In scale-free coupled circle mapping, the synchronization of each map and the extension of chaotic behavior can be controlled by changing the circle map parameters of the hub nodes. In this study, the set of parameter values of circle maps at hub nodes that leads to synchronization and expansion of the chaotic behavior of scale-free coupled circle maps would be elucidated.
Besicovich cascads and H¨older condition
Lema´nczyk, On the Hausdorf dimension of the set of closed orbits for the cylindrical transformation, Nonlinearity. A traditional method of qualitatively studying the dynamics of flows with a finite number of specific trajectories on surfaces consists of dividing the ambient manifold into regions with predictable trajectory behavior known as cells. We prove that the isomorphism class of this equipped multigraph is a complete topological invariant for our class of flows, and we also give a standard flow for each isomorphism class of equipped multigraphs.
On existence of one-dimensional Cantor type repeller on two-torus
Shub [4] there is an A-endomorphism of the circle whose non-erring set contains a basic set homeomorphic to the Cantor set. Plykin [1] that any one-dimensional basic set of an A-diffeomorphism of surfaces is locally homeomorphic to product of the Cantor set and the interval. We construct an A-endomorphism of two-torus whose non-wandering set contains one-dimensional repeller that is locally homeomorphic to product of the Cantor set and the interval.
Functional Iteration Models for Random Markets
There exists an endomorphism A of the two-torus which is not a diffeomorphism whose non-pervaded group consists of one-dimensional attractors and repulsors homeomorphic to the circle, and there exists an endomorphism A of the two-sphere whose non-sphere does not the haunted group contains repeller homeomorphic to some fractal group (such endomorphisms appear naturally in holomorphic dynamics).
Mastering high quality randomness via chaos theory
All NIST tests for dimensions 3 to 5 for each variable of this particular mesh pass, indicating that these realizations in 3-D to 5-D are good CPRNGs. Very long calculations are used on modern multi-core machines: they generate up to a hundred trillion iterations to evaluate such a network. To verify the portability of the computations on multicore architectures, we ran all our numerical experiments on several different multicore machines.
The TQ-bifurcations and generation of the T8N , T8P symbols
If the trajectories of a class(1) dynamical system contain T4◦ symbols and the system does not satisfy the conditions of the theorem, then proper time inversion is impossible for this system. The nature of the TQ bifurcations suggests that they define homogeneous dynamics regions of the system. If the trajectories of a class(1) dynamical system contain T4◦ symbols and the system does not satisfy the conditions of the theorem, then proper time inversion is impossible for this system.
The structure of dendrites and continuous maps on them
1 – the model of discretization of a continuous signal and the model of stroboscopic Poincare map; 2 – the model, from a certain point of view, of the most basic recurrent neural network. There are many examples of continuous maps on dendrites that show that dynamics of such maps depend on the structure of dendrites (see e.g. In the report the correlation between the structure of dendrites and dynamics of continuous maps on them is investigated.
On kneading constructions for invariant measures of discontinuous one-dimensional maps with zero entropy
We consider one-dimensional piecewise monotone discontinuous mappings with zero topological entropy and use the technique of invariant kneading and series kneading. In [1], [2], we used the kneading technique to study the properties of one-dimensional mappings with positive entropy and also their multidimensional perturbations. Nevertheless, if we consider Lorenz mappings with zero one-sided derivatives at the discontinuity point and with respect to the C1-topology, it is still integrally dependent on the mapping.
Transient sequences in a hypernetwork
On knee constructions for invariant measure of discontinuous one-dimensional maps with zero entropy discontinuous one-dimensional maps with zero entropy. Thurston for continuous piecewise monotone one-dimensional maps and was previously applied to maps with positive topological entropy. In the present discussion, we consider more complicated cases in a setting of a map with zero topological entropy.
We show how to use the kneading technique for zero-entropy Lorenz maps and for generalized interval exchange transformations, i.e. at the boundary of the convergence disk for kneading series in the complex plane, to construct the invariant measures and thus to construct semiconjugacy (which is actually a conjugacy in the transitive case) with minimal model maps of unit slope, i.e. for rigid interval exchange transformations. Regarding Lorenz maps in a quarter of a map with zero entropy, note that the entropy function can have jumps in C0 topology. Furthermore, for the class of Lorenz maps with zero one-sided derivatives at the discontinuity point and with C1 topology, such an extraordinary case is impossible, and the topological entropy therefore depends continuously on the map.
Maps in a laser harmonically mode-locked by optoelectronic feedback
Maslova et al., "Application of optoelectronic negative feedback to order the temporal structure of the diode-pumped Nd:YLF laser radiation", Bull. Gorbunkov et al., "Laser cavity round-trip time-scale regular and chaotic nonlinear dynamics in a picosecond laser controlled with the combination of positive and negative optoelectronic feedback". Maslova et al., "Period doubling cascade and deterministic chaos in a laser self-mode-locked by the combination of inertial negative and positive feedback", Bull.
Complex maps of exp(iz) kind: solitary and lattice coupled by linear relation
Indexn takes all values from adjacent cells for the current cell, which is not indexed. Nishio, “Effect of the Hub in Complex Networks of Coupled Parametrically Excited Oscillators with Dispersion,” Proceedings of IEEE Workshop on Nonlinear Circuit Networks (NCN'15), pp. National Supercomputing Center IT4Innovations, Department of the University of Ostrava, Institute for Research and Applications of Fuzzy Modeling.
Adiabatic cycles and geometric phases in maps
Here we then introduce a discrete analogue of the geometric phase and show that it is related to important aspects of map dynamics. In the case of maps with a twisted sine circle - a strongly dissipative system - we found an analytical relationship between the geometric phase and the rotation number of the map. For this, we further investigate the connection of the geometric phase with the rotation number as well as the role of the geometric phase in the onset of chaos.
Iterations of independent random flows generated by the differential equations with random parameters
If the mappings X·: Ω→ C(R+, C(E, E)) and T·: Ω→C(R+, B(H)) are measurable mappings of a measurable space into a topological space with a minimal algebra of subsets containing the topology, then the semigroups with one parameter X·,t, t ∈ R and T·(t), t∈R are random semigroups ([2]) of the mappings of the space E and H, respectively. In the article [1], a sufficient and necessary condition of the law was obtained of large numbers for the sequence of compositions of independent random semigroups of bounded linear operators. If the mappings X· : Ω→C(R+, C(E, E)) and T·: Ω→ C(R+, B(H)) are measurable mappings of a measurable space into a topological space with a minimal algebra of subsets containing the topology, then the one-parameter semigroups X·,t, t ∈ R, and T·(t), t ∈R are random semigroups ([2]) of mappings of the space E and H, respectively.
Non-equilibrium thermodynamics in the Poincar´e cycles
If for every ω ∈ Ω the maps Xω,t, t ≥ 0 are measurable maps of space (E,Λ, λ), then the single-parameter semigroupsTω(t), t∈R, of linear operators in spaceH are defined by the equalities (2) for each ω∈Ω. We investigate the limiting behavior of the mean composition series of independent random semigroups(X(t/n, ))n=Xωn(nt, )◦..◦Xω1(nt, ) in the space E and (T( t/n))n=Tωn(nt)◦..◦Tω1(nt) in spaceH. Each particle of the gas approaches arbitrarily close to the initial position infinitely many times.
Criteria for foliations with transverse linear connection to be pseudo-Riemannian and Riemannian
Criteria that foliations with transverse linear connection are pseudo-Riemann and Riemannian pseudo-Riemannian and Riemannian. For folations (M, F) with transverse parabolic geometry of rank one, the Riemannian criterion is known from [5]. We prove that the following criterion for foliations with cross-linear connection is pseudo-Riemannian.
Lyapunov’s exponents and
Currently, Riemannian sheets form the most deeply studied class of foils with transverse geometric structures. In the case when the dimension of (M, F) is zero, Theorem 1 implies that the Schmidt criterion for a torsion-free linear connection is the Levi-Civita connection for a pseudo-Riemannian metric [1]. As a corollary of Theorem 1, we obtain a necessary and sufficient condition for a foliation (M, F) with transverse linear connection to be Lorentzian.
The firefly algorithm (FA) was proposed by Yang in 2007 and is based on the idealized behavior of the flashing characteristics of fireflies [2–4]. In the case of firefly i, if the assignment of all objects does not change, the value of λi decreases. In the case of firecracker i, if the assignment of all objects does not change, the value of λi.
On locally linearizable billiard systems
Therefore, research on synchronization phenomena has been widely reported not only in the technical field, but also in the physical and biological field. In this study, we investigate synchronization phenomena observed in the ring-star system model of van der Pol oscillators through circuit experiments and computer simulation. We observe different types of synchronization phenomena by increasing the coupling strength of the ring.
Dynamics of monotone maps on a one-dimensional locally connected continuum
In this report, the dynamics of monotonic maps on a one-dimensional locally connected continuum are studied. Dynamics of monotonic graph, dendrite and dendroid maps, International Journal of Bifurcation and Chaos. Vaniukova On the sequence of non-wandering points of monotonic maps on local dendrites, Journal of Physics: Conference Series.
Boltzmann extremals and ergodic theorem for group representations
Vedenyapin, Kazantseva
The main problem of the ergodic theory is the problem of describing a limit, beyond which a solution of Liouville equation (the equation for density or for particle distribution functions) goes with time going to infinity. Such property, when any decreasing functionality is continuous, can be considered as the property of reversibility of the dynamics. We prove the existence of entropy and then the analogue of the H theorem for representations of groups: S([x])≥S(x).
Список литературы
Boltzmann: On the connection between the second law of the mechanical theory of heat and the probability theory in thermal equilibrium theorems., Selected papers, Nauka, M. Treschev: Weak convergence of solutions of the Liouville equation for nonlinear Hamiltonian systems, TMF, 2003, Volume 134, Number 3, Pages 388–400.
The Hamilton–Jacobi Method in the Non Hamiltonian Situation and Boltzmann extremals
The Hamilton-Jacobi method in the non-Hamiltonian situation and Boltzmann extrema and Boltzmann extrema. Hydrodynamic substitution, which is well known in the theory of the Vlasov equation [1]-[3], has recently been applied to the Liouville equation and Hamiltonian mechanics [4]-[8]. In [4]-[6], Kozlov outlined the simplest derivation of the Hamilton-Jacobi (HJ) equation, and the hydrodynamic substitution simply connected this derivation to Liouville's equation [7]-[8].
On the dynamics of non-invertible branched coverings of surfaces
The number of neurons in the hidden layer is smaller than that of the input and output layers. In this study, we emphasize the weight in the network due to the difference in the number of neurons in the hidden layer. As the number of neurons in the hidden layer decreases, all neurons work and express each other.
On pseudo-Anosov homeomorphisms with non-orietable invariant foliations
Geometric structures on orbifolds and their automorphisms
By analogy with manifolds we define the notion of an almost complex structure in orbifolds and obtain the following statement. Point out that solid geometries contain G-structure of finite type, Kartan geometry, and solid Gromov-sense geometries. This work was prepared within the framework of the Academic Fund Program at the Higher School of Economics of the National Research University (HSE) with grant No. and was supported within the framework of a subsidy granted to HSE by the Government of the Russian Federation for the implementation of the Global Program of Competitiveness.
An algorithm for the simulation of nonlinear oscillators
On the birth of separators in magnetic fields
List of Participants
The Conference NOMA-2017
