We show the existence of a local stable manifold for a bidirectional discrete-time nondiffeomorphic nonlinear Hamiltonian dynamics. This is the case where zero is a closed loop eigenvalue and therefore the Hamiltonian matrix is not invertible. In addition, we show the eigenstructure and the symplectic properties of the mixed direction nonlinear Hamiltonian dynamics. We extend the Local Stable M...

A unitarily invariant projective framework is introduced to analyze the complexity of path–following methods for the eigenvalue problem. A condition number, and its relation to the distance to ill–posedness, is given. A Newton map appropriate for this context is defined, and a version of Smale’s γ-Theorem is proven. The main result of this paper bounds the complexity of path–following methods i...

A maximum a posteriori probability (MAP) code acquisition scheme is proposed which utilizes all the available information by exploiting stochastic properties of spreading codes. Application of this method shows: i) code acquistion superiority of Bologna codes (Markov codes having eigenvalue of the transition probability matrix λ = √ 3 − 2) over independent and identically distributed (i.i.d.) c...

In the 1960s, Atkinson introduced an abstract algebraic setting for multiparameter eigenvalue problems. He showed that a nonsingular multiparameter eigenvalue problem is equivalent to the associated system of generalized eigenvalue problems. Many theoretical results and numerical methods for nonsingular multiparameter eigenvalue problems are based on this relation. In this paper, the above rela...

We consider the problem of showing that 1 is an eigenvalue for a family generalised transfer operators Farey map. This important in thermodynamic formalism approach to dynamical systems, which this particular case related spectral theory modular surface via Selberg Zeta function and zeta functions maps. After briefly recalling these connections, we show can be formulated on appropriate Hilbert ...

We analyze a class of piecewise linear parabolic maps on the torus, namely those obtained by considering a linear map with double eigenvalue one and taking modulo one in both components. We show that within this two parameter family of maps, the set of noninvertible maps is open and dense. For certain cases (where the entries in the matrix are rational) we show that the maximal invariant set ha...

We analyze a class of piecewise linear parabolic maps on the torus, namely those obtained by considering a linear map with double eigenvalue one and taking modulo one in both components. We show that within this two parameter family of maps, the set of noninvertible maps is open and dense. For certain cases (where the entries in the matrix are rational) we show that the maximal invariant set ha...

Consider the Cauchy problem for a strictly hyperbolic, N×N quasilinear system in one space dimension ut + A(u)ux = 0, u(0, x) = ū(x), (1) where u 7→ A(u) is a smooth matrix-valued map, and the initial data u is assumed to have small total variation. We investigate the rate of convergence of approximate solutions of (1) constructed by the Glimm scheme, under the assumption that, letting λk(u), r...

In this paper, it is shown that by exploiting the explicit parametric state feedback solution, it is feasible to obtain the ultimate solution to minimum sensitivity problem. A numerical algorithm for construction of a robust state feedback in eigenvalue assignment problem for a controllable linear system is presented. By using a generalized parametric vector companion form, the problem of eigen...