Piecewise linear maps, Liapunov exponents and entropy
نویسندگان
چکیده
منابع مشابه
Arithmetic Exponents in Piecewise-affine Planar Maps
We consider the growth of some indicators of arithmetical complexity of rational orbits of (piecewise) affine maps of the plane, with rational parameters. The exponential growth rates are expressed by a set of exponents; one exponent describes the growth rate of the so-called logarithmic height of the points of an orbit, while the others describe the growth rate of the size of such points, meas...
متن کاملTopological Entropy in the Synchronization of Piecewise Linear and Monotone Maps: Coupled Duffing oscillators
ACILINA CANECO Instituto Superior de Engenharia de Lisboa, Mathematics Unit, DEETC and CIMA-UE, Rua Conselheiro Emidio Navarro, 1, 1949-014 Lisboa, Portugal E-mail: [email protected] J. LEONEL ROCHA Instituto Superior de Engenharia de Lisboa, Mathematics Unit, DEQ, and CEAUL, Rua Conselheiro Emidio Navarro, 1, 1949-014 Lisboa, Portugal E-mail: [email protected] CLARA GRÁCIO Departm...
متن کاملDynamics of Piecewise Linear Discontinuous Maps
In this paper, the dynamics of maps representing classes of controlled sampled systems with backlash are examined. First, a bilinear one-dimensional map is considered, and the analysis shows that, depending on the value of the control parameter, all orbits originating in an attractive set are either periodic or dense on the attractor. Moreover, the dense orbits have sensitive dependence on init...
متن کاملLiapunov Exponents for Higher-order Linear Differential Equations Whose Characteristic Equations Have Variable Real Roots
We consider the linear differential equation n X k=0 ak(t)x (n−k)(t) = 0 t ≥ 0, n ≥ 2, where a0(t) ≡ 1, ak(t) are continuous bounded functions. Assuming that all the roots of the polynomial zn + a1(t)zn−1 + · · · + an(t) are real and satisfy the inequality rk(t) < γ for t ≥ 0 and k = 1, . . . , n, we prove that the solutions of the above equation satisfy |x(t)| ≤ const eγt for t ≥ 0.
متن کاملThe topological entropy of iterated piecewise affine maps is uncomputable
We show that it is impossible to compute (or even to approximate) the topological entropy of a continuous piecewise affine function in dimension four. The same result holds for saturated linear functions in unbounded dimension. We ask whether the topological entropy of a piecewise affine function is always a computable real number, and conversely whether every non-negative computable real numbe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2008
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2007.05.035