Publications
144 results found
Turaev D, 2016, Exponential energy growth due to slow parameter oscillations in quantum mechanical systems, Physical Review E, Vol: 93, ISSN: 1539-3755
It is shown that a periodic emergence and destruction of an additional quantum number leads to an exponential growth of energy of a quantum mechanical system subjected to a slow periodic variation of parameters. The main example is given by systems (e.g., quantum billiards and quantum graphs) with periodically divided configuration space. In special cases, the process can also lead to a long period of cooling that precedes the acceleration, and to the desertion of the states with a particular value of the quantum number.
Turaev D, Vladimirov AG, Zelik S, 2016, Interaction of Spatial and Temporal Cavity Solitons in Mode-Locked Lasers and Passive Cavities, International Conference Laser Optics (LO), Publisher: IEEE
Shah K, Gelfreich V, Rom-Kedar V, et al., 2015, Leaky Fermi accelerators, PHYSICAL REVIEW E, Vol: 91, ISSN: 1539-3755
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- Citations: 3
Turaev D, 2015, Maps close to identity and universal maps in the newhouse domain, Communications in Mathematical Physics, Vol: 335, Pages: 1235-1277, ISSN: 0010-3616
Given an n-dimensional C r-diffeomorphism g, its renormalized iteration is an iteration of g, restricted to a certain n-dimensional ball and taken in some C r-coordinates in which the ball acquires radius 1. We show that for any r ≥ 1 the renormalized iterations of C r-close to identity maps of an n-dimensional unit ball B n (n ≥ 2) form a residual set among all orientation-preserving C r-diffeomorphisms B n→ R n. In other words, any generic n-dimensional dynamical phenomenon can be obtained by iterations of C r-close to identity maps, with the same dimension of the phase space. As an application, we show that any C r-generic two-dimensional map that belongs to the Newhouse domain (i.e., it has a so-called wild hyperbolic set, so it is not uniformly-hyperbolic, nor uniformly partially-hyperbolic) and that neither contracts, nor expands areas, is C r-universal in the sense that its iterations, after an appropriate coordinate transformation, C r-approximate every orientation-preserving two-dimensional diffeomorphism arbitrarily well. In particular, every such universal map has an infinite set of coexisting hyperbolic attractors and repellers.
Pereira T, Turaev D, 2015, Exponential energy growth in adiabatically changing Hamiltonian systems, Physical Review E, Vol: 91, ISSN: 1539-3755
We show that the mixed phase space dynamics of a typical smooth Hamiltonian system universally leads to a sustained exponential growth of energy at a slow periodic variation of parameters. We build a model for this process in terms of geometric Brownian motion with a positive drift, and relate it to the steady entropy increase after each period of the parameters variation.
Pereira T, Turaev D, 2015, Fast Fermi Acceleration and Entropy Growth, MATHEMATICAL MODELLING OF NATURAL PHENOMENA, Vol: 10, Pages: 31-47, ISSN: 0973-5348
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- Citations: 4
Turaev D, 2014, Hyperbolic sets near homoclinic loops to a saddle for systems with a first integral, REGULAR & CHAOTIC DYNAMICS, Vol: 19, Pages: 681-693, ISSN: 1560-3547
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- Citations: 3
Gelfreich V, Rom-Kedar V, Turaev D, 2014, Oscillating mushrooms: adiabatic theory for a non-ergodic system, Journal of Physics A - Mathematical and Theoretical, Vol: 47, ISSN: 1751-8113
Can elliptic islands contribute to sustained energy growth as parameters of aHamiltonian system slowly vary with time? In this paper we show that a mushroombilliard with a periodically oscillating boundary accelerates the particleinside it exponentially fast. We provide an estimate for the rate ofacceleration. Our numerical experiments confirms the theory. We suggest that asimilar mechanism applies to general systems with mixed phase space.
Gonchenko A, Gonchenko S, Kazakov A, et al., 2014, Simple Scenarios of Onset of Chaos in Three-Dimensional Maps, INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, Vol: 24, ISSN: 0218-1274
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- Citations: 40
Shilnikov AL, Turaev DV, Lerman LM, et al., 2014, Leonid Pavlovich Shilnikov, INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, Vol: 24, ISSN: 0218-1274
Shilnikov LP, Shilnikov AL, Turaev DV, 2014, Showcase of Blue Sky Catastrophes, INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, Vol: 24, ISSN: 0218-1274
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- Citations: 12
Afraimovich VS, Gonchenko SV, Lerman LM, et al., 2014, Scientific heritage of LP Shilnikov, REGULAR & CHAOTIC DYNAMICS, Vol: 19, Pages: 435-460, ISSN: 1560-3547
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- Citations: 30
Turaev DV, Warner C, Zelik S, 2014, Energy growth for a nonlinear oscillator coupled to a monochromatic wave, REGULAR & CHAOTIC DYNAMICS, Vol: 19, Pages: 513-522, ISSN: 1560-3547
Gelfreich V, Turaev D, 2014, Arnold Diffusion in a priory chaotic Hamiltonian systems
We assume that a symplectic real-analytic map has an invariant normallyhyperbolic cylinder and an associated transverse homoclinic cylinder. It iswell known that such cylinder is preserved under small perturbations. We provethat for a generic real- analytic perturbation of this map the boundaries ofthe cylinder are connected by trajectories of the perturbed map.
Gonchenko SV, Lamb JSW, Rios I, et al., 2014, Attractors and repellers near generic elliptic points of reversible maps, DOKLADY MATHEMATICS, Vol: 89, Pages: 65-67, ISSN: 1064-5624
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- Citations: 12
Gonchenko SV, Gonchenko AS, Ovsyannikov II, et al., 2013, Examples of Lorenz-like Attractors in Henon-like Maps, MATHEMATICAL MODELLING OF NATURAL PHENOMENA, Vol: 8, Pages: 48-70, ISSN: 0973-5348
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- Citations: 22
Gelfreich V, Rom-Kedar V, Turaev D, 2012, Fermi acceleration and adiabatic invariants for non-autonomous billiards, CHAOS, Vol: 22, ISSN: 1054-1500
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- Citations: 41
Gonchenko SV, Ovsyannikov II, Turaev D, 2012, On the effect of invisibility of stable periodic orbits at homoclinic bifurcations, PHYSICA D-NONLINEAR PHENOMENA, Vol: 241, Pages: 1115-1122, ISSN: 0167-2789
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- Citations: 8
Turaev D, Vladimirov AG, Zelik S, 2012, Long-Range Interaction and Synchronization of Oscillating Dissipative Solitons, PHYSICAL REVIEW LETTERS, Vol: 108, ISSN: 0031-9007
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- Citations: 63
Rom-Kedar V, Turaev D, 2012, Billiards: A singular perturbation limit of smooth Hamiltonian flows, CHAOS, Vol: 22, ISSN: 1054-1500
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- Citations: 13
Lerman LM, Turaev D, 2012, Breakdown of symmetry in reversible systems, REGULAR & CHAOTIC DYNAMICS, Vol: 17, Pages: 318-336, ISSN: 1560-3547
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- Citations: 18
Anosov DV, Afraimovich VS, Bunimovich LA, et al., 2012, Leonid Pavlovich Shil'nikov (obituary), RUSSIAN MATHEMATICAL SURVEYS, Vol: 67, Pages: 573-577, ISSN: 0036-0279
Tlidi M, Vladimirov AG, Turaev D, 2011, Mobility properties of 2D cavity solitons in systems with delayed feedback
Vladimirov AG, Turaev D, Zelik S, 2011, Synchronization of interacting temporal cavity oscillons
Vladimirov AG, Turaev D, Zelik S, 2011, Synchronization of interacting temporal cavity oscillons
Temporal cavity solitons (TCS) - localized dissipative structures of light propagating along the longitudinal axis of coherently driven optical cavities - are very promising for applications in telecommunication technology. In a recent work [1] formation and interactions of TCS in a standard silica fiber cavity were studied experimentally. Here we present a theoretical investigation of the interaction of the TCS within the framework of the Lugiato-Lefever (LL) model. Major attention is given to the interaction of oscillating solitons above a self-pulsing instability threshold and to the effect of external periodic modulations on the soliton interactions. © 2011 IEEE.
Tlidi M, Vladimirov AG, Turaev D, 2011, Mobility properties of 2D cavity solitons in systems with delayed feedback
Significant advances have been made recently in the study of transverse localized structures of light known also as dissipative optical solitons. This was largely due to the potential applications of optical localized structures as bits for information storage and processing. Although in general their properties are relatively well understood, the investigation of the effect of the delayed feedback on the dynamics of optical systems, which exhibit transverse dissipative solitons, is a relatively new area of research [1-4]. © 2011 IEEE.
Tigan G, Turaev D, 2011, Analytical search for homoclinic bifurcations in the Shimizu-Morioka model, PHYSICA D-NONLINEAR PHENOMENA, Vol: 240, Pages: 985-989, ISSN: 0167-2789
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- Citations: 36
Turaev D, 2011, Diffeomorphisms which cannot be topologically conjugate to diffeomorphisms of a higher smoothness, ERGODIC THEORY AND DYNAMICAL SYSTEMS, Vol: 31, Pages: 563-569, ISSN: 0143-3857
Gelfreich V, Rom-Kedar V, Shah K, et al., 2011, Robust Exponential Acceleration in Time-Dependent Billiards, PHYSICAL REVIEW LETTERS, Vol: 106, ISSN: 0031-9007
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- Citations: 47
Turaev D, 2011, Richness of chaos in the absolute Newhouse domain, Publisher: Hackensack, NJ: World Scientific; New Delhi: Hindustan Book Agency, Pages: 1804-1815
We show that universal maps (i.e. such whose iterations approximate everypossible dynamics arbitrarily well) form a residual subset in an open set in the space ofsmooth dynamical systems. The result implies that many dynamical systems emergingin natural applications may, on a very long time scale, have quite unexpected dynamicalproperties, like coexistence of many non-trivial hyperbolic attractors and repellers andattractors with all zero Lyapunov exponents. Applications to reversible and symplecticmaps are also considered.
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