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Residual Minimizing Model Reduction for Parameterized Nonlinear Dynamical Systems
nonlinear dynamical systems nonlinear equations parameterized models
2011/1/17
We present a method for approximating the solution of a parameterized, nonlinear dynamical (or static) system using an affine combination of solutions computed at other points in the input parameter s...
Justification of the Dynamical Systems Method (DSM) for global homeomorphisms
The Dynamical Systems Method (DSM) surjectivity global homeomorphisms
2011/1/21
The Dynamical Systems Method (DSM) is justified for solving oper-ator equations F(u) = f, where F is a nonlinear operator in a Hilbert space H.
A note on dynamical systems defining Jacobi's theta-constants
Jacobi’s theta-constants modular forms Poisson structures
2011/1/19
We propose a system of ordinary differential equations which defines Jacobi’s theta-constant series. The relations of this system to the classical Darboux–Halphen equations and equations introduced by...
Transience in Dynamical Systems
Equilibrium states thermodynamic formalism transience interval maps
2010/12/6
We extend the theory of transience to general dynamical systems with no Markov structure assumed. This is linked to the theory of phase transitions. We also provide examples of new kinds of transient ...
On the Complete Integrability of Nonlinear Dynamical Systems on Discrete Manifolds within the Gradient-Holonomic Approach
Exactly Solvable and Integrable Systems (nlin.SI) Mathematical Physics (math-ph)
2010/11/10
A gradient-holonomic approach for the Lax type integrability analysis of differentialdiscrete dynamical systems is devised. The asymptotical solutions to the related Lax equation are studied, the rela...
On dynamical systems and phase transitions for $Q+1$-state $P$-adic Potts model on the Cayley tree
dynamical systems phase transitions
2010/11/11
In the present paper, we introduce a new kind of $p$-adic measures for $q+1$-state Potts model, called {\it $p$-adic quasi Gibbs measure}. For such a model, we derive a recursive relations with respe...
Spectral triples for hyperbolic dynamical systems
Spectral triples hyperbolic dynamical systems
2010/11/19
Spectral triples are defined for C*-algebras associated with hyperbolic dynamical systems known as Smale spaces. The spectral dimension of one of these spectral triples is shown to recover the topolog...
Entropy Formulas For Dynamical Systems With Mistakes
Entropy Formulas Dynamical Systems Mistakes
2010/11/11
We study the recurrence to mistake dynamical balls, that is, dynamical balls that admit some errors and whose proportion of errors decrease tends to zero with the length of the dynamical ball. We prov...
Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems
Entropic Fluctuations Statistical Mechanics I. Classical Dynamical Systems
2010/12/8
Within the abstract framework of dynamical system theory we describe a general approach to the
Transient (or Evans-Searles) and Steady State (or Gallavotti-Cohen) Fluctuation Theorems of non-equilibr...
Right submodules of finite rank for von Neumann dynamical systems
Finite rank submodules von Neumann dynamical systems
2010/11/29
Let (M, , , ) be a (finite) von Neumann dynamical system and let N be a unital von Neumann subalgebra of M which is -invariant. If V ⊂ L2(M) is a right N-submodule whose pr...
On tensor products of weak mixing vector sequences and their applications to C*-dynamical systems
Uniform weak mixing weak mixing ergodicity
2010/11/29
We prove that, under certain conditions, uniform weak mixing (to zero)of the bounded sequences in Banach space implies uniform weak mixing of its tensor product. Moreover, we prove that ergodicity of ...
K-Theoretic Duality for Hyperbolic Dynamical Systems
K-Theoretic Duality Hyperbolic Dynamical Systems
2010/12/13
The K-theoretic analog of Spanier-Whitehead duality for noncommutative C-algebras is shown to hold for the Ruelle algebras associated to irreducible Smale spaces.This had previously been proved only ...
Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems
Entropic Fluctuations Statistical Mechanics I. Classical Dynamical Systems
2010/12/16
Within the abstract framework of dynamical system theory we describe a general approach to the
Transient (or Evans-Searles) and Steady State (or Gallavotti-Cohen) Fluctuation Theorems of non-equilibr...
Multicanonical Sampling of Rare Trajectories in Chaotic Dynamical Systems
Rare Trajectories Chaotic Dynamical Systems
2010/4/2
In chaotic dynamical systems, a number of rare trajectories with low level of chaoticity are embedded in chaotic sea, while extraordinary unstable trajectories can exist even in weakly chaotic regions...
We introduce one dimensional sets to help describe and constrain the integral curves of an $n$ dimensional dynamical system. These curves provide more information about the system than the zero-dimens...