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Simple Spectrum for Tensor Products of Mixing Map Powers
Tensor Products Mixing Map Powers Dynamical Systems
2011/9/20
Abstract: We prove the existence of a mixing rank one map $T$ such that the product $T\otimes T^2\otimes T^3\otimes...$ has simple spectrum. This result is used in S.V. Thikhonov's proof of the existe...
Shrinking Targets for Countable Markov Maps
Countable Markov Maps Shrinking Targets Dynamical Systems
2011/9/20
Abstract: Let $T$ be an expanding Markov map with a countable number of inverse branches and a repeller $\Lambda$ contained within the unit interval. Given $\alpha \in \R_+$ we consider the set of poi...
Reducibility of cocycles under a Brjuno-Russmann arithmetical condition
Brjuno-Russmann arithmetical condition Dynamical Systems
2011/9/19
Abstract: The arithmetics of the frequency and of the rotation number play a fun- damental role in the study of reducibility of analytic quasi-periodic cocycles which are sufficiently close to a const...
Higher cohomology for Anosov actions on certain homogeneous spaces
Higher cohomology Anosov actions certain homogeneous spaces
2011/9/19
Abstract: We study the smooth untwisted cohomology with real coefficients for the action on [SL(2, R) \times \cdot \cdot \cdot \times SL(2, R)]/{\Gamma} by the subgroup of diagonal matrices, where {\G...
Connecting orbits for families of Tonelli Hamiltonians
families of Tonelli Hamiltonians Dynamical Systems
2011/9/19
Abstract: We investigate the existence of Arnold diffusion-type orbits for systems obtained by iterating in any order the flows of a family of Tonelli Hamiltonians. Our approach is close to the one of...
Random fields on model sets with localized dependency and their diffraction
Diffraction Pure point spectrum Absolutely continuous spectrum Quasicrystal Model set
2011/9/19
Abstract: For a random field on a general discrete set, we introduce a condition that the range of the correlation from each site is within a predefined compact set D. For such a random field {\omega}...
About the trajectory synthesis to go back to nominal mode for a class of hybrid systems
hybrid automata reachability linear vector fields state-space
2011/9/19
Abstract: This paper presents basis parts of a new method to synthesize a return trajectory for a reactive process from a default mode to one of the nominal modes. The process is modeled with a hybrid...
Existence of a Lorenz renormalization fixed point of an arbitrary critical order
Lorenz renormalization fixed point arbitrary critical order Dynamical Systems
2011/9/19
Abstract: We present a proof of the existence of a renormalization fixed point for Lorenz maps of the simplest non-unimodal combinatorial type ({0,1},{1,0,0}), and with a critical point of arbitrary o...
Creation of Homoclinic Tangencies in Hamiltonians by the Suspension of Poincaré Sections
Hamiltonian vector field Anosov flow elliptic point homoclinic tangency
2011/9/16
Abstract: In this note we show that for any Hamiltonian defined on a symplectic 4-manifold M and any point p in M, there exists a C2-close Hamiltonian whose regular energy surface through p is either ...
Asymptotic Stability of Dissipated Hamilton-Poisson Systems
dynamical systems stability theory rigid body
2011/9/16
Abstract: We will further develop the study of the dissipation for a Hamilton-Poisson system introduced in \cite{2}. We will give a tensorial form of this dissipation and show that it preserves the Ha...
Sharkovskii order for non-wandering points
Sharkovskii order transfer principles Dynamical Systems
2011/9/15
Abstract: For a map $f:I \rightarrow I$, a point $x \in I$ is periodic with period $p \in \mathbb{N}$ if $f^p(x)=x$ and $f^j(x)\not=x$ for all $0
Integration of Constraint Equations in Problems of a Disc and a Ball Rolling on a Horizontal Plane
Integration of Constraint Equations Disc Ball Rolling Horizontal Plane Dynamical Systems
2011/10/9
Abstract: The problem of a disc and a ball rolling on a horizontal plane without slipping is considered. Differential constrained equations are shown to be integrated when the trajectory of the point ...
Bernoulli equilibrium states for surface diffeomorphisms
Equilibrium measures Countable Markov partitions Bernoulli
2011/9/14
Abstract: Suppose f is a $C^{1+\alpha}$ surface diffeomorphism, and m is an equilibrium measure of a Holder continuous potential. We show that if m has positive metric entropy, then f is measure theor...
Liouville-Arnold integrability of the pentagram map on closed polygons
Liouville-Arnold integrability closed polygons Dynamical Systems
2011/9/14
Abstract: The pentagram map is a discrete dynamical system defined on the moduli space of polygons in the projective plane. This map has recently attracted a considerable interest, mostly because its ...
Embedding smooth and formal diffeomorphisms through the Jordan-Chevalley decomposition
local diffeomorphism normal form embedding flow
2011/9/14
Abstract: In [Xiang Zhang, The embedding flows of $C^{\infty}$ hyperbolic diffeomorphisms, J. Differential Equations 250 (2011), no. 5, 2283-2298] Zhang proved that any local smooth hyperbolic diffeom...