Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Finitude of Physical Measures for Random Maps
 
Pablo G. Barrientos Instituto de Matemá e Estatíca, Universidade Federal Fluminense, Niterói, Brazil
Fumihiko Nakamura Kitami Institute of Technology, Hokkaido, Japan
Yushi Nakano Hokkaido University, Hokkaido, Japan
Hisayoshi Tokoyawa Kitami Institute of Technology, Hokkaido, Japan
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-37905-214-9
Product Code:  AST/459
List Price: $69.00
AMS Member Price: $55.20
Please note AMS points can not be used for this product
Click above image for expanded view
Finitude of Physical Measures for Random Maps
Pablo G. Barrientos Instituto de Matemá e Estatíca, Universidade Federal Fluminense, Niterói, Brazil
Fumihiko Nakamura Kitami Institute of Technology, Hokkaido, Japan
Yushi Nakano Hokkaido University, Hokkaido, Japan
Hisayoshi Tokoyawa Kitami Institute of Technology, Hokkaido, Japan
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-37905-214-9
Product Code:  AST/459
List Price: $69.00
AMS Member Price: $55.20
Please note AMS points can not be used for this product
  • Book Details
     
     
    Astérisque
    Volume: 4592025; 103 pp
    MSC: Primary 37; Secondary 60

    For random compositions of independent and identically distributed measurable maps on a Polish space, the authors study the existence and finitude of absolutely continuous ergodic stationary probability measures (which are, in particular, physical measures) whose basins of attraction cover the whole space almost everywhere. The authors characterize and hierarchize such random maps in terms of their associated Markov operators, as well as show the difference between classes in the hierarchy by plenty of examples, including additive noise, multiplicative noise, and iterated function systems.

    The authors also provide sufficient practical conditions for a random map to belong to these classes. For instance, they establish that any continuous random map on a compact Riemannian manifold with absolutely continuous transition probability has finitely many physical measures whose basins of attraction cover the manifold Lebesgue almost everywhere.

    A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

    Readership

    Graduate students and research mathematicians.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
Volume: 4592025; 103 pp
MSC: Primary 37; Secondary 60

For random compositions of independent and identically distributed measurable maps on a Polish space, the authors study the existence and finitude of absolutely continuous ergodic stationary probability measures (which are, in particular, physical measures) whose basins of attraction cover the whole space almost everywhere. The authors characterize and hierarchize such random maps in terms of their associated Markov operators, as well as show the difference between classes in the hierarchy by plenty of examples, including additive noise, multiplicative noise, and iterated function systems.

The authors also provide sufficient practical conditions for a random map to belong to these classes. For instance, they establish that any continuous random map on a compact Riemannian manifold with absolutely continuous transition probability has finitely many physical measures whose basins of attraction cover the manifold Lebesgue almost everywhere.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians.

Review Copy – for publishers of book reviews
Please select which format for which you are requesting permissions.