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Riesz measures and Wishart laws associated to quadratic maps
convex cones homogeneous cones Riesz measures Wishart laws
2011/8/22
Abstract: We introduce a natural definition of Riesz measures and Wishart laws associated to an $\Omega$-positive (virtual) quadratic map, where $\Omega \subset \real^n$ is a regular open convex cone....
Time--Evolving Statistics of Chaotic Orbits of Conservative Maps in the Context of the Central Limit Theorem
time Chaotic Orbits Conservative Maps Central Limit Theorem Statistics
2011/7/6
We study chaotic orbits of conservative low--dimensional maps and present numerical results showing that the probability density functions (pdfs) of the sum of $N$ iterates in the large $N$ limit exhi...
Shared inputs and desynchrony in elliptic bursters: from slow passage to discontinuous circle maps
Dynamical Systems (math.DS) Chaotic Dynamics (nlin.CD)
2010/11/10
What input signals will lead to synchrony vs. desynchrony in a group of biological oscillators? This question connects with both classical dynamical sys- tems analyses of entrainment and phase locking...
Global return maps for mixed-mode oscillations with one fast and two slow variables
Dynamical Systems (math.DS) Classical Analysis and ODEs (math.CA) Chaotic Dynamics (nlin.CD)
2010/11/10
Alternating patterns of small and large amplitude oscillations occur in a wide variety of physical, chemical, biological and engineering systems. These mixed-mode oscillations (MMOs) are often found i...
Involutivity of integrals for sine-Gordon, modified KdV and potential KdV maps
Exactly Solvable and Integrable Systems (nlin.SI)
2010/11/10
Closed form expressions in terms of multi-sums of products have been given for integrals of sine-Gordon, modi?ed Korteweg-de Vries and potential Korteweg-de Vries maps obtained as (p,-1)-traveling wav...