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48 results on '"LUZZATTO, S."'

1. SRB measures for partially hyperbolic systems whose central direction is weakly expanding

Author

Alves, Jose F., Dias, C. L., Luzzatto, S., and Pinheiro, V.

Subjects
Mathematics - Dynamical Systems
Abstract

We consider partially hyperbolic \( C^{1+} \) diffeomorphisms of compact Riemannian manifolds of arbitrary dimension which admit a partially hyperbolic tangent bundle decomposition \( E^s\oplus E^{cu} \). Assuming the existence of a set of positive Lebesgue measure on which \( f \) satisfies a weak nonuniform expansivity assumption in the centre~unstable direction, we prove that there exists at most a finite number of transitive attractors each of which supports an SRB measure. As part of our argument, we prove that each attractor admits a Gibbs-Markov-Young geometric structure with integrable return times. We also characterize in this setting SRB measures which are liftable to Gibbs-Markov-Young structures., Comment: Revised version

Published
2014

2. Statistical properties of one-dimensional maps with critical points and singularities

Author

Díaz-Ordaz, K., Holland, M. P., and Luzzatto, S.

Subjects
Mathematics - Dynamical Systems, 37D50, 37A25
Abstract

We prove that a class of one-dimensional maps with an arbitrary number of non-degenerate critical and singular points admits an induced Markov tower with exponential return time asymptotics. In particular the map has an absolutely continuous invariant probability measure with exponential decay of correlations for H\"{o}lder observations., Comment: 31 pages

Published
2007

3. Markov structures and decay of correlations for non-uniformly expanding dynamical systems

Author

Alves, J. F., Luzzatto, S., and Pinheiro, V.

Subjects
Mathematics - Dynamical Systems, 37A25, 37C40, 37D25
Abstract

We consider non-uniformly expanding maps on compact Riemannian manifolds of arbitrary dimension, possibly having discontinuities and/or critical sets, and show that under some general conditions they admit an induced Markov tower structure for which the decay of the return time function can be controlled in terms of the time generic points need to achieve some uniform expanding behavior. As a consequence we obtain some rates for the decay of correlations of those maps and conditions for the validity of the Central Limit Theorem., Comment: 24 pages

Published
2002

5. Introduzione

Author

LUZZATTO S, PEDULLA', Gabriele, LUZZATTO S PEDULLA' G DE VINCENTIIS A, Luzzatto, S, and Pedulla', Gabriele

Published
2010

8. A Frobenius Theorem for Corank-1 Continuous Distributions in Dimension 2 and 3

Author

Tureli, S, Luzzatto, S, and War, KM

Subjects
General Mathematics, 0101 Pure Mathematics
Abstract

We formulate a notion of (uniform) asymptotic involutivity and show that it implies (unique) integrability of two-dimensional continuous distributions in dimension three. This generalizes a classi- cal theorem of Frobenius Theorem which says that an involutive C1 distribution is uniquely integrable.

Published
2016

9. A Frobenius Theorem for Continuous Distributions in Dimension Three

Author

Luzzatto, S, Tureli, S, and War, K

Subjects
Dynamical systems, Analysis of PDEs, Differential geometry
Abstract

We formulate a notion of (uniform) asymptotic involutivity and show that it implies (unique) integrability of corank-1 continuous distributions in dimensions three or less. This generalizes and extends a classical theorem of Frobenius Theorem which says that an involutive C^1 distribution is uniquely integrable.

Published
2016

17. V.4. Dynamical systems.

Author

Lamb, J. and Luzzatto, S.

Subjects
DYNAMICAL systems, APPLIED mathematics, DETERMINISTIC processes, MANIFOLDS (Mathematics), DIFFERENTIAL geometry
Published
2010

19. L'età del benessere

Author

PEDULLA', Gabriele, LUZZATTO S, PEDULLA' G, SCARPA D, and Pedulla', Gabriele

Published
2012

20. L'immacolato d'Annunzio

Author

Benzoni, Pietro, Luzzatto, S., Pedullà, G., Scarpa, D., and Taal- en Letterkunde

Subjects
dannunzianesimo, Narcissism, D'Annunzio, History of Italian Litterature, Saba
Abstract

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Published
2012

21. Il contestatore Johnny

Author

PEDULLA', Gabriele, LUZZATTO S, PEDULLA' G, SCARPA D, and Pedulla', Gabriele

Published
2012

22. Walter Scott in Italia

Author

IRACE E, PEDULLA', Gabriele, LUZZATTO S, PEDULLA' G, SCARPA D, Irace, E, and Pedulla', Gabriele

Published
2012

26. Paladini d'argilla

Author

PEDULLA', Gabriele, LUZZATTO S PEDULLA' G IRACE E, and Pedulla', Gabriele

Published
2011

27. L'età di Roma

Author

PEDULLA', Gabriele, LUZZATTO S PEDULLA' G IRACE E, and Pedulla', Gabriele

Published
2011

28. Annio, il falsario di Dio

Author

PEDULLA', Gabriele, LUZZATTO S PEDULLA' G DE VINCENTIIS A, and Pedulla', Gabriele

Published
2010

29. Scipione e i tiranni

Author

PEDULLA', Gabriele, LUZZATTO S PEDULLA' G DE VINCENTIIS A, and Pedulla', Gabriele

Published
2010

31. Disputare con il 'Principe'

Author

PEDULLA', Gabriele, LUZZATTO S PEDULLA' G DE VINCENTIIS A, and Pedulla', Gabriele

Published
2010

33. Sulle tracce degli antichi?

Author

PEDULLA', Gabriele, LUZZATTO S PEDULLA' G DE VINCENTIIS A, and Pedulla', Gabriele

Published
2010

36. L'età di Firenze

Author

PEDULLA', Gabriele, LUZZATTO S PEDULLA' G DE VINCENTIIS A, and Pedulla', Gabriele

Published
2010

37. L'età di Padova

Author

PEDULLA', Gabriele, LUZZATTO S PEDULLA' G DE VINCENTIIS A, and Pedulla', Gabriele

Published
2010

38. Terragni Giuseppe

Author

NICOLOSO, PAOLO, DE GRAZIA V., LUZZATTO S. A CURA DI, and Nicoloso, Paolo

Published
2003

39. Ponti Gio

Author

NICOLOSO, PAOLO, DE GRAZIA V., LUZZATTO S. A CURA DI, and Nicoloso, Paolo

Published
2003

40. SALERNO, SVOLTA DI

Author

PONS S, DE GRAZIA V, LUZZATTO S, and Pons, S

Published
2003

42. STALIN

Author

PONS S, DE GRAZIA V, LUZZATTO S, and Pons, S

Published
2003

43. Piacentini Marcello

Author

Nicoloso, Paolo, DE GRAZIA V., LUZZATTO S., and Nicoloso, Paolo

Published
2003

44. Triennale di Milano

Author

NICOLOSO, PAOLO, DE GRAZIA V., LUZZATTO S. A CURA DI, and Nicoloso, Paolo

Published
2003

45. Urbanistica

Author

NICOLOSO, PAOLO, DE GRAZIA V., LUZZATTO S., and Nicoloso, Paolo

Published
2003

47. Armamenti

Author

Knox, MacGregor, Luzzatto, S., and De Grazia, V.

Subjects
H Social Sciences (General), JA Political science (General)
Published
2002

48. Rigorous numerics for critical orbits in the quadratic family.

Author

Golmakani A, Koudjinan CE, Luzzatto S, and Pilarczyk P

Abstract

We develop algorithms and techniques to compute rigorous bounds for finite pieces of orbits of the critical points, for intervals of parameter values, in the quadratic family of one-dimensional maps f a (x)=a-x 2 . We illustrate the effectiveness of our approach by constructing a dynamically defined partition P of the parameter interval Ω=[1.4,2] into almost 4×10 6 subintervals, for each of which we compute to high precision the orbits of the critical points up to some time N and other dynamically relevant quantities, several of which can vary greatly, possibly spanning several orders of magnitude. We also subdivide P into a family P + of intervals, which we call stochastic intervals, and a family P - of intervals, which we call regular intervals. We numerically prove that each interval ω∈P + has an escape time, which roughly means that some iterate of the critical point taken over all the parameters in ω has considerable width in the phase space. This suggests, in turn, that most parameters belonging to the intervals in P + are stochastic and most parameters belonging to the intervals in P - are regular, thus the names. We prove that the intervals in P + occupy almost 90% of the total measure of Ω. The software and the data are freely available at http://www.pawelpilarczyk.com/quadr/, and a web page is provided for carrying out the calculations. The ideas and procedures can be easily generalized to apply to other parameterized families of dynamical systems.

Published
2020
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