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## Action-Minimizing Invariant Measures for Tonelli Lagrangians

*Alfonso Sorrentino*

### in Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691164502
- eISBN:
- 9781400866618
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691164502.003.0003
- Subject:
- Mathematics, Applied Mathematics

This chapter discusses the notion of action-minimizing measures, recalling the needed measure–theoretical material. In particular, this allows the definition of a first family of invariant sets, the ... More

## Action-Minimizing Curves for Tonelli Lagrangians

*Alfonso Sorrentino*

### in Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691164502
- eISBN:
- 9781400866618
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691164502.003.0004
- Subject:
- Mathematics, Applied Mathematics

This chapter discusses the notion of action-minimizing orbits. In particular, it defines the other two families of invariant sets, the so-called Aubry and Mañé sets. It explains their main dynamical ... More

## The Hamilton-Jacobi Equation and Weak KAM Theory

*Alfonso Sorrentino*

### in Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691164502
- eISBN:
- 9781400866618
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691164502.003.0005
- Subject:
- Mathematics, Applied Mathematics

This chapter describes another interesting approach to the study of invariant sets provided by the so-called weak KAM theory, developed by Albert Fathi. This approach can be considered as the ... More

## Invariant Measures and Ergodicity

*Gopinath Kallianpur and P. Sundar*

### in Stochastic Analysis and Diffusion Processes

- Published in print:
- 2014
- Published Online:
- April 2014
- ISBN:
- 9780199657063
- eISBN:
- 9780191781759
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199657063.003.0011
- Subject:
- Mathematics, Probability / Statistics, Applied Mathematics

Existence of stationary measures and ergodic behavior of stochastic systems form an active and important research area with several applications in engineering, physical and biological sciences. A ... More

## Coordination Control for Multiagent Interconnected Systems

*Wassim M. Haddad and Sergey G. Nersesov*

### in Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691153469
- eISBN:
- 9781400842667
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691153469.003.0007
- Subject:
- Mathematics, Applied Mathematics

This chapter describes a stability and control design framework for time-varying and time-invariant sets of nonlinear dynamical systems. The framework is applied to the problem of coordination ... More

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