In 2000, T. Uno and M. Yagiura published an algorithm that computes all the K common intervals of two given permutations of length n in O(n + K) time. Our paper first presents a decomposition approach to obtain a compact encoding for common intervals of d permutations. Then, we revisit T. Uno and M. Yagiura’s algorithm to yield a linear time algorithm for finding this encoding. Besides, we adap...

We consider piecewise monotone maps of the interval with zero entropy or no periodic points. First, we give a rigid model for these maps: the interval translations mappings, possibly with ips. It follows, e.g., that the complexity of a piecewise monotone map of the interval is at most polynomial if and only if this map has a nite number of periodic points up to monotone equivalence. Second, we ...

In this paper we consider a class of d-interval exchange transformations, which we call the symmetric class. For this class we define a new self-dual induction process in which the system is successively induced on a union of sub-intervals. This algorithm gives rise to an underlying graph structure which reflects the dynamical behavior of the system, through the Rokhlin towers of the induced ma...

This paper focuses on the invariance control problem for discrete-time switched nonlinear systems. The proposed approach computes controlled invariant sets in a finite number of iterations and directly yields a partitionbased invariance controller using the information recorded during the computation. In contrast with Lyapunov-based control methods, this method does not require the subsystems t...

bifurcations leading to chaos have been investigated in a number of one dimensional dynamical systems by varying the parameters incorporated within the systems. the property hyperbolicity has been studied in detail in each case which has significant characteristic behaviours for regular and chaotic evolutions. in the process, the calculations for invariant set have also been carried out. a bro...

let g_1 and g_2 be simple connected graphs with disjoint vertex sets v(g_1) and v(g_2), respectively. for given vertices a_1in v(g_1) and a_2in v(g_2), a splice of g_1 and g_2 by vertices a_1 and a_2 is defined by identifying the vertices a_1 and a_2 in the :union: of g_1 and g_2. in this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.

Since 2005 a new powerful invariant of an algebra has emerged using the earlier work of Horvath, Hethelyi, Kulshammer and Murray. The authors studied Morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. It was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...

The method of invariant manifolds was originally developed for hyperbolic rest points of autonomous equations. It was then extended from fixed points to arbitrary solutions and from autonomous equations to nonautonomous dynamical systems by either the Lyapunov–Perron approach or Hadamard’s graph transformation. We go one step further and study meaningful notions of hyperbolicity and stable and ...

since 2005 a new powerful invariant of an algebra has emerged using the earlier work of horvath, hethelyi, kulshammer and murray. the authors studied morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. it was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modi ed version o...