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Measures of the full Hausdorff dimension for a general Sierpinski carpet
Sofic measure Sierpinski carpet matrix-valued potential Gibbs measure a-weighted thermodynamic formalism
2012/6/21
The measure of the full dimension for a general Sierpi\'{n}ski carpet is studied. In the first part of this study, we give a criterion for the measure of the full Hausdorff dimension of a Sierpi\'{n}s...
Regularization of the Kepler problem on the Sphere
Regularization of the Kepler problem the Sphere Dynamical Systems
2012/6/29
In this paper we regularize the Kepler problem on $S^3$ in several different ways. First, we perform a Moser-type regularization. Then, we adapt the Ligon-Schaaf regularization to our problem. Finally...
Hopf bifurcation with zero frequency and imperfect SO(2) symmetry
Hopf bifurcation zero frequency imperfect SO(2) symmetry Dynamical Systems
2012/6/29
Rotating waves are periodic solutions in SO(2) equivariant dynamical systems. Their precession frequency changes with parameters and it may change sign, passing through zero. When this happens, the dy...
Multifractal analysis of some multiple ergodic averages for the systems with non-constant Lyapunov exponents
Multifractal analysis of some multiple ergodic averages non-constant Lyapunov exponents Dynamical Systems
2012/6/27
We study certain multiple ergodic averages of an iterated functions system generated by two contractions on the unit interval. By using the dynamical coding ${0,1}^{\mathbb{N}}$ of the attractor, we c...
Reduction of Interaction Delays in Networks
Reduction of Interaction Delays Networks Dynamical Systems
2012/6/21
Delayed interactions are a common property of coupled natural systems. For instance, signals in neural or laser networks propagate at finite speed giving rise to delayed connections. Such systems are ...
An Alternative Approach to Generalised BV and the Application to Expanding Interval Maps
Generalised bounded variation transfer operator expanding map spectral gap
2012/6/21
We introduce a family of Banach spaces of measures, each containing the set of measures with density of bounded variation. These spaces are suitable for the study of weighted transfer operators of pie...
In the nineties, Michel Herman conjectured the existence of a positive measure set of invariant tori at an elliptic diophantine critical point of a hamiltonian function. I prove a generalisation of th...
Expanding Semiflows on Branched Surfaces and One-Parameter Semigroups of Operators
Expanding Semiflows Branched Surfaces One-Parameter Semigroups of Operators Dynamical Systems
2012/6/25
We consider expanding semiflows on branched surfaces. The family of transfer operators associated to the semiflow is a one-parameter semigroup of operators. The transfer operators may also be viewed a...
Discrete-Time Chaotic-Map Truly Random Number Generators: Design, Implementation, and Variability Analysis of the Zigzag Map
Truly Random Number Generator Current-Mode Circuits Switched-Current Technique Variability
2012/6/21
In this paper, we introduce a novel discrete chaotic map named zigzag map that demonstrates excellent chaotic behaviors and can be utilized in Truly Random Number Generators (TRNGs). We comprehensivel...
A Smale space is a chaotic dynamical system with canonical coordinates of contracting and expanding directions. The basic sets for Smale's Axiom A systems are a key class of examples. We consider the ...
A Characterization of Cellular Automata Generated by Idempotents on the Full Shift
cellular automata marker lemma products of idempotents decidability
2012/6/19
In this article, we discuss the family of cellular automata generated by so-called idempotent cellular automata (CA G such that G^2 = G) on the full shift. We prove a characterization of products of i...
Aperiodic Sequences and Aperiodic Geodesics
Recurrence Bernoulli-shift Geodesic Flow Flow-invariant Sets Symbolic Dynamics
2012/6/19
We introduce a quantitative condition on orbits of dynamical systems which measures their aperiodicity. We show the existence of sequences in the Bernoulli-shift and geodesics on closed hyperbolic man...
Lowering topological entropy over subsets revisited
entropy principal extension lowerable hereditarily lowerable
2012/6/19
Let $(X, T)$ be a topological dynamical system. Denote by $h (T, K)$ and $h^B (T, K)$ the covering entropy and dimensional entropy of $K\subseteq X$, respectively. $(X, T)$ is called D-{\it lowerable}...
A Brouwer fixed point theorem for graph endomorphisms
Graph theory graph endormorphisms Lefschetz number Euler characteristic Brouwer fixed point Dynamical zeta function
2012/6/21
We prove a Lefschetz formula for general simple graphs which equates the Lefschetz number L(T) of an endomorphism T with the sum of the degrees i(x) of simplices in G which are fixed by T. The degree ...
Generalized Riesz Products on the Bohr compactification of $\R$
Generalized Riesz products almost periodic functions Bohr compactification mean value Besicovitch space Kac Central Limit Theorem Kakutani criterion
2012/6/19
We study a class of generalized Riesz products connected to the spectral type of some class of rank one flows on $\R$. Applying a Central Limit Theorem of Kac, we exhibit a large class of singular gen...